## Electromagnetic Waves

## Electromagnetic Waves Introduction

Maxwell formulated a set of equations involving electric and magnetic fields, and their sources, the charge and current densities. These equations are known as Maxwell’s equations. Together with the Lorentz force formula, they mathematically express all the basic laws of electromagnetism. The most important prediction to emerge from Maxwell’s equations is the existence of electromagnetic waves, which are (coupled) time-varying electric and magnetic fields that propagate in space. The speed of the waves, according to these equations, turned out to be very close to the speed of light (3 × 10^{8} m/s), obtained from optical measurements. This led to the remarkable conclusion that light is an electromagnetic wave. Maxwell’s work thus unified the domain of electricity, magnetism, and light, Hertz, in 1885, experimentally demonstrated the existence of electromagnetic waves. Its technological use by Marconi and others led in due course to the revolution in communication that we are witnessing today.

In this unit, we first discuss the need for displacement current and its consequences. Then we present a descriptive account of electromagnetic waves. The broad spectrum electromagnetic waves stretch from γ rays (wavelength ~ 10^{-12} m) to long radio waves (wavelength ~ 10^{6} m)

## Displacement Current

We have seen that an electrical current produces a magnetic field around it. Maxwell showed that for logical consistency, a changing electric field must also produce a magnetic field. This effect is of great importance because it explains the existence of radio waves, gamma rays, and visible light, as well as all other forms of electromagnetic waves.

To see how a changing electric field gives rise to a magnetic field, let us consider the process of charging a capacitor and apply Ampere’s circuital law given by

⇒ \(\int \mid B . d l=\mu_0(t)\)…….(1)

Figure 1 (a) shows parallel plate capacitor C, a part of a circuit through which a time-dependent current i (t) flows. Let us find the magnetic field at a point such as P, in a region outside the parallel plate capacitor.

For this, we consider a plane circular loop of radius r whose plane is perpendicular to the direction of the current-carrying wire, and which is centered symmetrically concerning the wire.

From symmetry, the magnetic field is directed along the circumference of the circular loop and is the same in magnitude at all points on the loop so if B is the magnitude of the field, the left side of equation. (1) is B (2πr). So we have

B (2πr) = μ_{0}i (t) ……… (2)

Now, consider a different surface, which has the same boundary. This is a pot-like surface (Fig.1 (b)] that nowhere touches the current, but has its bottom between the capacitor plates; its mouth is a circular loop and is shaped like a tiffin box (without the lid) [Fig. 1 (b)].

On applying Ampere’s circuital law to such a surface with the same perimeter, we find that the left-hand side of Eq. (1) has not changed but the right-hand side is zero and not μ_{0}i since no current passes through the surface of Fig 1 (b).

So we have a contradiction; calculated one way, there is a magnetic field at a point P; calculated another way, the magnetic field at P is zero. Since the contradiction arises from our use of Ampere’s circuital law, this law must be missing something. The missing term must be such that one gets the same magnetic field at point P, no matter what surface is used.

We can guess the missing term by looking carefully at Fig. 1 (b). Is there anything passing through the surface S between the plates of the capacitor? Yes, of course, the electric flux. If the capacitor platescitor has an area A, and a total charge Q, the magnitude of the electric field E between the plates is (Q/A)/ ε_{0}. The field is perpendicular to the surface S of Fig.1 (b). It has the over the area A of the capacitor plates and vanishes outside it. So the electric flux ΦE through the surface S is found using Gauss’s law, is given by,

⇒ \(\Phi_{\mathrm{E}}=|\mathrm{E}| \quad \mathrm{A}=\frac{1}{\varepsilon_0} \frac{\mathrm{Q}}{\mathrm{A}} \quad \mathrm{A}=\frac{\mathrm{Q}}{\varepsilon_0}\)………… (3)

Now if the charge Q on the capacitor plates changes with time, there is a current i = (dQ / dt), so that using Eq. (3), we have

E d

⇒ \(\frac{\mathrm{d} \Phi_{\mathrm{E}}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\frac{\mathrm{Q}}{\varepsilon_0}\right)=\frac{1}{\varepsilon_0} \frac{\mathrm{dQ}}{\mathrm{dt}}\)

This implies that for consistency, the additional current should be

⇒ \(\varepsilon_0\left(\frac{d \Phi_E}{d t}\right)=\mathrm{i}_{\mathrm{d}}\)…………. (4)

This is the missing term in Ampere’s circuital law. If we generalize amperes law by adding to the current carried by conductors through the surface, another term which is ε_{0}times the rate of change of electric flux through the same surface, the total current has the same value for all surfaces. If this is done, there is no contradiction in the value of B obtained anywhere using the generalized Amper’s law.

B at the point P is non-zero no matter which surface is used for calculating it. B at point P outside the plates [Fig.1 (a)] is the same as at point M just inside, as it should be. The current carried by conductors due to the flow of charges is called conduction current. The current, given by Eq. (4), is a new term and is due to time changing electric field (or electric displacement, ε_{0}E).

It is therefore called displacement current or Maxwell’s displacement current. Figure 2 shows the electric and magnetic fields inside the parallel plates capacitor discussed above. The generalization made by Maxwell then is the following.

The source of a magnetic field is not just the conduction of electric current due to flowing charges, but also the time rate of change of the electric field. More precisely, the total current i is the sum of the conduction current denoted by iC, and the displacement current denoted by id( = ε_{0}(dΦΕ)/ dt). So we have

⇒ \(\mathrm{i}=\mathrm{i}_{\mathrm{c}}+\mathrm{i}_{\mathrm{d}}=\mathrm{i}_{\mathrm{c}}+\varepsilon_0 \frac{\mathrm{d} \Phi_{\mathrm{E}}}{\mathrm{dt}}\)………… (5)

Figure 2 continuity of electric current i = i_{C} + la outside condenser it only ic and inside it is only id

In explicit terms, this means that outside the capacitor plates, we have only conduction current i_{C}= i, and no displacement current, i.e., i_{D}= 0. On the other hand, inside the capacitor, there is no conduction current, i.e., i_{C}= 0, and there is only displacement current, so that i_{D}= i.

The generalized (and correct) Ampere’s circuital law has the same form as Eq, (1), with one difference: ” the total current passing through any surface of which the closed loop is the perimeter” is the sum of the conduction current and the displacement current The generalized law is

⇒ \(\int \mathrm{B} \bullet \mathrm{d} \ell=\mu_0 \mathrm{i}_{\mathrm{c}}+\mu_0 \varepsilon_0 \frac{\mathrm{d} \Phi_{\mathrm{E}}}{\mathrm{dt}}\)……….. (6)

and is known as Ampere-Maxwell’s law.

In all respects, the displacement current has the same physical effects as the conduction current. In some cases, for example, steady electric fields in a conducting wire, the displacement current may be zero since the electric field E does not change with time.

In other cases, for example, the charging capacitor above, both conduction and displacement currents may be present in different regions of space. In most of the cases, they both may be present in the same region of space, as there exists no perfectly conducting or perfectly insulating medium.

Most interestingly, there may be large regions of space where there is no conduction current, but there is only a displacement current due to time-varying electric fields. In such a region, we expect a magnetic field, though there is no (conduction) current source nearby.

The prediction of such a displacement current can be verified experimentally. For example, a magnetic field (say at point M) between the plates of the capacitor in Fig. 3 can be measured and is seen to be the same as that just outside (at P).

The displacement current has (literally) far-reaching consequences. One thing we immediately notice is that the laws of electricity and magnetism are now more symmetrical.

The time-dependent electric and magnetic fields give rise to each other. Faraday’s law of electromagnetic induction and Ampere-Maxwell law give a quantitative expression of this statement, with the current being the total current as in Eq. (5). One very important consequence of this symmetry is the existence of electromagnetic waves, which we discuss qualitatively in the next section.

**Maxwell’s Equations**

⇒ \(\int \overrightarrow{\mathrm{E}} \bullet \overrightarrow{\mathrm{dA}}=\mathrm{Q} / \varepsilon_0\) ………7(a) (Gauss’s Law for electricity)

⇒ \(\int \vec{B} \bullet \overrightarrow{d A}=0\) ………7(b) (Gauss’s Law for magnetism)

⇒ \(\int \overrightarrow{\mathrm{E}} \bullet \overrightarrow{\mathrm{d} \ell}=\frac{-\mathrm{d} \Phi_{\mathrm{B}}}{\mathrm{dt}}\) ………7(c) (Faraday’s Laws of electromagnetic induction)

⇒ \(\int \vec{B} \cdot \vec{d} \ell=\mu_0 i_c+\mu_0 \varepsilon_0 \frac{d \Phi_E}{d t}\) ………7(d) (Ampere – Maxwell Law)

**Solved Examples**

**Example 1. A parallel plate capacitor with circular plates of radius 1 m has a capacitance of 1 nF. At t = 0, it is connected for charging in series with a resistor R = 1 M Ω across a 2 V battery (as shown). Calculate the magnetic field at a point P. halfway between the center and the periphery of the plates, after t = 10 ^{-3} s. (The charge on the capacitor at time t is q (t) = CV [1 – exp (–t / τ)], where the time constant τ is equal to CR)**

**Solution:**

The time constant of the CR circuit is τ = CR = 10^{-3} s. Then we have

q(t) = CV [1 – exp (–t/ τ)]

= 2 × 10^{-9}[1– exp (– t/ 10^{-3})]

The electric field in between the plates at time t is

⇒ \(\mathrm{E}=\frac{\mathrm{q}(\mathrm{t})}{\varepsilon_0 \mathrm{~A}}=\frac{\mathrm{q}}{\pi \varepsilon_0}\) A = π (1)2 m2 = area of the plates. ………(1)

Consider now a circular loop of radius (1 / 2) m parallel to the plates passing through P. The magnetic field B at all points on the loop is along the loop and of the same value. The flux ΦE through this loop is

ΦE= E × area of the loop

⇒ \(=\mathrm{E} \times \pi \times\left(\frac{1}{2}\right)^2=\frac{\pi \mathrm{E}}{4}=\frac{\mathrm{q}}{4 \varepsilon_0}\)………(ii) follows from (i) 0

The displacement current

⇒ \(\mathrm{i}_{\mathrm{d}}=\varepsilon_0 \frac{\mathrm{d} \Phi_{\mathrm{E}}}{\mathrm{dt}}=\frac{1}{4} \frac{\mathrm{dq}}{\mathrm{dt}}\)= 0.5 × 10–6 exp (–1)

at t = 10^{-3} s. Now, applying the Ampere-Maxwell law to the loop, we get 1

B × 2π × \(\left(\frac{1}{2}\right)\)….(= μ_{0}(ic+ id) = μ_{0}(0 + i_{d}) = 0.5 × 10^{-6} μ_{0}exp (–1) ^{2}

or, B = 0.74 × 10^{-3 }T

**Electromagnetic Waves**

From equation 7(c) it follows that time time-varying magnetic field produces an electric field. Whereas Equation 7(d) follows that time time-varying electric field produces a magnetic field. In the case of oscillating charge both electric and magnetic fields are oscillating. Consider a loop of wire carrying alternating current.

This will generate a circulating time-varying (sinusoidal) magnetic field normal to the current loop as shown in figure 3. This time-varying sinusoidal magnetic field in turn shall give rise to the circulating electric field. The electric field lines will be perpendicular to circulating magnetic field lines. One field generates the other. Consequently, continuous induction and speeding electric and magnetic fields occur.

**Sources of electromagnetic waves**

How are electromagnetic waves produced? Neither stationary charges Nor charges in uniform motion (steady currents) can be sources of electromagnetic waves. The former produces only an electrostatic field, while the latter produces magnetic fields that, however, do not vary with time. It is an important result of Maxwell’s theory that accelerated charges radiate electromagnetic waves.

An oscillating charge generates harmonic electric and magnetic fields. Hence it is a source of electromagnetic waves. Oscillating charge radiates electromagnetic energy in the form of EM waves. As an electron transiting from a higher energy state to a lower energy state in an atom generates time-varying pervades electric and magnetic fields and hence radiates energy in the form of electromagnetic waves (light)

- AC loop generates a time-varying magnetic field.
- Generation of E-M waves

The proof of this basic result is beyond the scope of this text, but we can accept it based on rough qualitative reasoning. Consider a charge oscillating with some frequency. (An oscillating charge is an example of an accelerating charge.)

This produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of oscillating electric field, and so on. The oscillating electric and magnetic fields regenerate each other thus the waves propagate through the space. The frequency of electromagnetic waves naturally equals the frequency of oscillation of the charge.

The energy associated with the propagating wave comes at the expense of the energy of the source accelerated charge. When are electron transits from a higher energy state to a lower energy state in are atom. The transiting electron generates oscillating electric and magnetic fields. The difference in energy between the two levels comes out of an electromagnetic wave. Light is thus an e.m.wave

**Nature of electromagnetic wave**

It can be shown from Maxwell’s equations that electric and magnetic fields in an electromagnetic wave are perpendicular to each other and the direction of propagation. It appears reasonable. In Fig 4, we show a typical example of a plane electromagnetic wave propagating along the z direction (the fields are shown as a function of the z coordinate, at a given time t). The electric field exists along the x-axis, and varies Sinusoidal with z, at a given time. The magnetic field Byis along the y-axis and again varies Sinusoidal with z. The electric and magnetic fields Exand Byare perpendicular to each other, and to the direction z of propagation. EM waves are transverse. We can write Exand By as follows :

E_{x}= E_{0}sin (kz – ωt) ………… 8(a)

B_{y}= B_{0}sin (kz – ωt) ………… 8 (b)

Here k is related to the wavelength λ of the wave by the usual equation

⇒ \(\mathrm{k}=\frac{2 \pi}{\lambda}\)………… (9)

and ω is the angular frequency. k is the magnitude of the wave vector (or propagation vector) direction and describes the direction of propagation of the wave.

The speed of propagation of the wave is (ω/k). Using Eqs. [8 (a) and (b)] For Expand By and Maxwell’s equation we find that

Transverse Nature of EM waves. E and B are mutually perpendicular and perpendicular to the direction of propagation. (E_{B} const × = K )

ω = ck, where, c = 1 /\(\sqrt{\mu_0 \varepsilon_0}\) ……….. (10)

The relation ω = ck is the standard one for waves. This relation is often written in terms of frequency. ν (=ω/ 2π) and wavelength. λ (= 2π / k) as

2πν = \(\mathrm{c}\left(\frac{2 \pi}{\lambda}\right)\) Or

νλ = c ……….. (11)

It follows from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as

⇒ \(\frac{E_0}{B_0}=c\) ……….(12)

In a material medium, the total electric and magnetic fields inside a medium are described in terms of permittivity ε and magnetic permeability μ (These describe the factors by which the total fields differ from the external fields). These replace ε_{0}and μ_{0}in the description of electric and magnetic fields in Maxwell’s equation in free space with the result that in a material medium of permittivity ε and magnetic permeability μ, the velocity of light becomes,

υ =\(v=\frac{1}{\sqrt{\mu \varepsilon}}\)…………. (13)

In a medium and consequently \(\frac{E}{B}\) =υ…………. (14)

**(2) Refractive index:** The velocity of light depends on the electric and magnetic properties of the medium. The velocity of electromagnetic waves in free space or vacuum is an important fundamental constant. It has been shown by experiments on electromagnetic waves of different wavelengths that this velocity in free space is the same (independent of wavelength)

The refractive index is defined as the ratio of the speed of light in a vacuum to its velocity in the medium, therefore,

Refractive index \(\mathrm{n}=\frac{\mathrm{c}}{\mathrm{v}}=\sqrt{\frac{\mu}{\mu_0} \frac{\varepsilon}{\varepsilon_0}}=\sqrt{\varepsilon_{\mathrm{r}}}\) …………(15)

εr is the relative permittivity or dielectric constant of the medium

**(3) Energy and Momentum:** Do electromagnetic waves carry energy and momentum like other waves? Yes, they do. In a region of free space with electric field E, there is an electric energy density

⇒ \(\mathrm{U}_{\mathrm{E}}=\frac{\varepsilon_0 \mathrm{E}^2}{2}\left(\mathrm{~J} / \mathrm{m}^3\right)\) ……16(a)

Similarly, as seen associated with a magnetic field B a magnetic energy density is given by

⇒ \(U_B=\frac{B^2}{2 \mu_0}\left(\mathrm{~J} / \mathrm{m}^3\right)\) ……..16(b)

As electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with them. Now consider a plane perpendicular to the direction of propagation electromagnetic wave (Fig. 4).

If there are, on this plane, electric charges these will be set to sustained motion by electric and magnetic fields of the electromagnetic wave. The charges thus acquire energy and momentum from the waves.

This just illustrates the fact that an electromagnetic wave (like other waves.) carries energy and momentum light carries energy from the sun to the earth, thus making life possible on the Earth.

**(4) Radiation pressure:** Since it carries momentum, an electromagnetic wave also exerts pressure called radiation pressure. If the total energy transferred to a surface in time t is U. It can be shown that the magnitude of the total momentum delivered to this surface (for complete absorption) is,

⇒ \(p=\frac{U}{C} \text {, }\)and ……..17(a)

⇒ \(p=\frac{2 U}{c}\) for perfectly reflecting surface. ……..17(b)

**(5) Poynting vector: **It is vector-directed along the line of propagation of electromagnetic waves. Its magnitude is equal to the amount of energy flowing per unit of time, per unit area perpendicular to an electromagnetic wave.

S = \(\vec{S}=\frac{\vec{E} \times \vec{B}}{\mu_0}\) ……..18 0

This is also the intensity of the propagating electromagnetic wave

**Solved Examples**

**Example 2. A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, E = 6.3 **

**Solution:**

Using Eq. (8.10), the magnitude of B is

⇒ \(B=\frac{E}{c}=\frac{6.3 V / m}{3 \times 10^8 \mathrm{~m} / \mathrm{s}}=2.1 \times 10^{-8} \mathrm{~T}\)

To find the direction, we note that E is along the y-direction and the wave propagates along the x-axis. Therefore, B should be in a direction perpendicular to both x- and y-axes. Using vector algebra, E × B should be along the x-direction. Since, Thus, B = 2.1 × 10^{-8} ˆ kT

Thus, B is along the z-direction

**Example 3. The magnetic field in a plane electromagnetic wave is given by By= 2 × 10 ^{-7} sin (0.5 × 103 x + 1.5 × 1011t) T.**

**What is the wavelength and frequency of the wave?****Write an expression for the electric field.**

**Solution:**

Comparing the given equation with

⇒ \(B_y=B_0 \sin \left[2 \pi\left(\frac{x}{y}+\frac{t}{T}\right)\right]\)

we get, λ =\(\lambda=\frac{2 \pi}{0.5 \times 10^3} \mathrm{~m}\) = 1.26 cm,

and \(\frac{1}{\mathrm{~T}}\)= ν = (1.5 × 10^{11}) / 2π = 23.9 GHz

E0= B0c = 2 × 10^{-7} T × 3 × 10^{8} m/s = 60 V/m

The electric field is perpendicular to the direction of propagation and the direction of the magnetic field. Therefore, the electric field along the z-axis is obtained as

Ez= 60 sin (0.5 × 10^{3 }x + 1.5 × 10^{11 }t) V/m

**Example 4. Light with an energy flux of 18 W/cm2falls on a non-reflecting surface at normal incidence. If the surface has an area of 20 cm2, find the average force exerted on the surface during 30 minutes. **

**Solution:**

The total energy falling on the surface is

U = (18 W/cm^{2}) × (20cm^{2}) × (30 × 60)

= 6.48 × 105 J

Therefore, the total momentum delivered (for complete absorption) is

⇒ p \(=\frac{U}{C}=\frac{6.48 \times 10^5 \mathrm{~J}}{3 \times 10^8 \mathrm{~m} / \mathrm{s}}=2.16 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}\)

The average force exerted on the surface is

F = \(\frac{p}{t}=\frac{2.16 \times 10^{-3}}{0.18 \times 14^4}=1.2 \times 10^{-6} \mathrm{~N}\)

**Example 5. Calculate the electric and magnetic fields produced by the radiation coming from a 100 W bulb at a distance of 3 m. Assume that the efficiency of the bulb is 2.5% and it is a point source.
Solution:**

The bulb, as a point source, radiates light in all directions uniformly. At a distance of 3 m, the surface area of the surrounding sphere is

A = 4πr^{2} = 4π(3)2 = 113 m^{2}

The intensity at this distance is

I =\(\frac{\text { Power }}{\text { Area }}=\frac{100 \mathrm{~W} \times 2.5 \%}{113 \mathrm{~m}^2}=0.022 \mathrm{~W} / \mathrm{m}^2\)

On average half of this intensity is provided by the electric field and half by the magnetic field.

⇒ \(\frac{1}{2} I=\frac{1}{2}\left(\varepsilon_0 E_{r m s}^2 c\right)=\frac{1}{2}\left(0.022 \mathrm{~W} / \mathrm{m}^2\right)\)

⇒ \(E_{\mathrm{mss}}=\sqrt{\frac{0.022}{\left(8.85 \times 10^{-12}\right)\left(3 \times 10^8\right)}} \mathrm{V} / \mathrm{m}=2.9 \mathrm{~V} / \mathrm{m}\)

The value of E found above is the root mean square value of the electric field. Since the electric field in a light beam is sinusoidal, the peak electric field is

⇒ \(E_0=\sqrt{2} E_{\mathrm{rms}}=\sqrt{2} \times 2.9 \mathrm{~V} / \mathrm{m}=4.07 \mathrm{~V} / \mathrm{m}\)

The electric field strength of light is fairly large

⇒ \(B_{r m s}=\frac{E_{\mathrm{ms}}}{c}=\frac{2.9 \mathrm{Vm}^{-1}}{3 \times 10^8 \mathrm{~ms}^{-1}}=9.6 \times 10^{-9} \mathrm{~T}\)

Again, since the field in the light beam is sinusoidal, the peak magnetic field is B0= 2Brms = 1.4 × 10–8 T. Note that although the energy in the magnetic field is equal to the energy in the electric field, the magnetic field is very weak.

**Electromagnetic Spectrum**

At the time Maxwell predicted the existence of electromagnetic waves, the only familiar electromagnetic waves were the visible light waves. The existence of ultraviolet and infrared waves was barely established. By the end of the nineteenth century, X-rays and gamma rays had also been discovered.

We now know that electromagnetic waves include visible light waves, X-rays gamma rays, radio waves, microwaves, ultraviolet and infrared waves. The classification of electromagnetic waves according to frequency in the electromagnetic spectrum is shown in Table 1 along with applications.

There is no sharp division between one kind of wave and the next. The classification is based roughly on how the waves are produced and/or detected.

**Table 1****: Summaries various bands of the electromagnetic spectrum, their origin, and ****detection**

**Table 2: Describes various applications of the frequency bands**

## Electromagnetic Waves Exercise – 1

**Question 1. The displacement current was first postulated by**

- Ampere
- Maxwell
- Hertz
- Marconi

**Answer:** 2. Maxwell

**Question 2. The fundamental source of e.m. waves**

- Is varying magnetic field
- Constant magnetic and electric fields
- Oscillations of electric charge
- Are planets

**Answer:** 3. Oscillations of electric charge

**Question 3. An accelerated electric charge emits**

- β – rays
- γ – rays
- e.m. waves
- None of the above

**Answer:** 3. e.m. waves

**Question 4. Electromagnetic waves in nature are**

- Longitudinal
- Longitudinal stationary
- Transverse
- Transverse – stationary

**Answer:** 3. Longitudinal stationary

**Question 5. The speed of e.m. waves is given by the relation**

- μ
_{0}ε_{0} - \(\sqrt{\mu_0 \varepsilon_0}\)
- 1/μ
_{0}ε_{0} - \(1/\sqrt{\mu_0 \varepsilon_0}\)

**Answer:** 4. \(1/\sqrt{\mu_0 \varepsilon_0}\)

**Question 6. Choose the only wrong statement from the following about electromagnetic waves**

- Are transverse
- Travels free space at the speed of light
- Are produced by accelerating charges
- Travel with the same speed in all media

**Answer:** 4. Travel with the same speed in all media

**Question 7. Electromagnetic waves**

- Are longitudinal waves
- Travel in free space at the speed of light
- Are produced by charges moving with uniform velocity
- Travel with the same speed in all media

**Answer:** 2. Travel in free space at the speed of light

**Question 8. An accelerated charge**

- Emits an electromagnetic wave
- Produces stationary electric and magnetic fields
- Produces a gravitational field
- None of the above

**Answer:** 1. Emits an electromagnetic wave

**Question 9. Ιn an electromagnetic wave, electric field E and magnetic field B are**

- Mutually perpendicular to each other
- All parallel
- At 300 each other
- Depends upon polarization

**Answer:** 1. Mutually perpendicular to each other

**Question 10. If E and B are the electric and magnetic fields of electromagnetic waves, then the direction of propagation of e. m. wave is along the direction of**

- E
- B
- E × Β
- None of the above

**Answer:** 3. E × Β

**Question 11. Which of the following pairs of space and time-varying E and B fields would generate a plane electromagnetic wave traveling in the Z– Z-direction**

- Ex, By
- Ey, Bx
- Ex, Bz
- Ez, Bx

**Answer:** 1. Ex, By

**Question 12. Electromagnetic waves obey the principle of**

- superposition
- Interference
- 1 and 2 both
- None of the above

**Answer:** 3. 1 and 2 both

**Question 13. Hertz produced electromagnetic waves by using**

- L C R circuit
- C R circuit
- L C circuit
- None of the above

**Answer:** 3. L C circuit

**Question 14. Choose the correct statement about electromagnetic waves**

- They are supersonic waves
- They are the electrically charged particles
- They travel with the speed of light
- They can only be produced in a laboratory.

**Answer:** 3. They travel with the speed of light

**Question 15. The visible range of light has a wavelength in cm is**

- 3 × 10
^{-6 }to 10^{-10} - 7 × 10
^{-5 }to 4 × 10^{-5} - 4 × 10
^{-5 }to 3 × 10^{-6} - 6 x 10
^{4 }to 1.5 × 103

**Answer:** 2. 7 × 10^{-5 }to 4 × 10^{-5}

**Question 16. The following electromagnetic waves have the shortest wavelength**

- γ – rays
- x – rays
- Ultraviolet rays
- Microwaves

**Answer:** 1. γ – rays

**Question 17. Which of the following has the longest wavelength `**

- Infrared light
- Ultraviolet light
- Microwaves
- X–rays

**Answer:** 3. Microwaves

**Question 18. Only microwaves are used for**

- Television
- Radio transmission
- Radar system
- All the above

**Answer:** 3. Radar system

**Question 19. The Earth’s atmosphere is richer than **

- Infrared radiation
- Ultraviolet radiations
- Visible radiations
- Blue color radiations

**Answer:** 1. Infrared radiation

**Question 20. The greenhouse effect is due to**

- Visible radiations
- Red color radiation
- Green color radiation
- Infrared radiation

**Answer:** 4. Infrared radiation

**Question 21. The greenhouse effect keeps the earth’s surface**

- COld in night
- Dusty and cold
- Warm in night
- Moist in night

**Answer:** 3. Warm at night

**Question 22. The ozone layer protects the living organism from**

- Ultraviolet radiations
- Infrared radiation
- X–rays
- All the radiations

**Answer:** 1. Ultraviolet radiations

**Question 23. Practically ozone layer absorbs the radiation of wavelength**

- Less than 3 x 10
^{-7}m - Greater than 3 x 10
^{-7}m - Equal to 3 x 10
^{-7}m - All the above

**Answer:** 1. Less than 3 x 10^{-7} m

**Question 24. The frequency of a wave is 6 × 10 ^{15} Hz. The wave is**

- Radioactive
- Microwave
- X-rays
- Ultraviolet

**Answer:** 4. Ultraviolet

**Question 25. If the wavelength of light is 4000 Å, then the number of waves in 1 mm length will be**

- 25
- 0.25
- 0. 25 × 10
^{4} - 25 × 10
^{4}

**Answer: **3. 0. 25 × 10^{4}

**Question 26. What is the range of frequency for ultrasonic waves?**

- 1kHz
- 5kHz
- 50 kHz
- 10 kHz

**Answer:**** **3. 50 kHz

**Question 27. If c is the speed of electromagnetic waves in vacuum, its speed v in a medium of dielectric constant k and relative permeability μr is**

- \(v=\frac{1}{\sqrt{\mu_r k}}\)
- \(v=c \sqrt{\mu_r k}\)
- \(v=\frac{c}{\sqrt{\mu_r k}}\)
- \(v=\frac{k}{\sqrt{\mu_r c}}\)

**Answer:** 3. \(v=\frac{c}{\sqrt{\mu_r k}}\)

**Question 28. Which one of the following is not an electromagnetic wave?**

- X-rays
- Gamma rays
- Cathode rays
- Infrared rays

**Answer:** 3. Cathode rays

**Question 29. The dimensions of \(\frac{1}{2}\)ε _{0} E^{2}(ε_{0}: permittivity of free space; E : electric field) is**

- M L T
^{-1} - M L
^{2}T^{-2} - M L
^{-1}T^{-2} - M L
^{2}T^{-1}

**Answer:** 3. M L^{-1} T^{-2}

**Question 30. The speed of electromagnetic waves in a vacuum**

- Depends upon the source of radiation
- Increases as we move from γ-rays to radio waves
- Decreases as we move from γ-rays to radiowaves
- Is the same for all of them

**Answer:** 4. Is the same for all of them

**Question 31. If λν, λx, and λmrepresent the wavelengths of visible light, x-rays and microwave respectively then**

- λm> λx> λν
- λν> λm> λx
- λυ> λx> λm
- λm> λν> λx

**Answer:** 4. λm> λν> λx

**Question 32. The frequency of the light wave in a material is 2 × 10 ^{14} Hz and the wavelength is 5000 Å. The refractive index of the material will be :**

- 1.40
- 1.50
- 3.00
- 1.33

**Answer:** 3. 3.00

**Question 33. The electric and magnetic fields of an electromagnetic wave are :**

- In phase and parallel to each other
- In opposite phase and perpendicular to each other
- In opposite phases and parallel to each other
- In phase and perpendicular to each other.

**Answer:** 4. In phase and perpendicular to each other.

**Question 34. The velocity of electromagnetic radiation in a medium of permittivity ε _{0} and permeability μ_{0}is given by :**

- \(\sqrt{\frac{\varepsilon_0}{\mu_0}}\)
- \(\sqrt{\mu_0 \varepsilon_0}\)
- \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)
- \(\sqrt{\frac{\mu_0}{\varepsilon_0}}\)

**Answer:** 3. \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)

**Question 35. Which of the following is the infrared wavelength?**

- 10
^{-4}cm - 10
^{-5}cm - 10
^{-6}cm - 10
^{-7}cm

**Answer:** 1. 10^{-4} cm

**Question 36. According to Maxwell’s hypothesis, a changing electric field gives rise to**

- An e.m.f
- Electric current
- Magnetic field
- Pressure gradient

**Answer:** 3. Magnetic field

**Question 37. Maxwell in his famous equation of electromagnetism introduced the concept of**

- a.c. current
- d.c. current
- Displacement current
- Impedance

**Answer:** 3. Displacement current

**Question 38. Sodium lamps are used in foggy conditions because**

- yellow light is scattered less by the fog particles
- yellow light is scattered more by the fog particles
- yellow light is unaffected during its passage through the fog
- wavelength of yellow light is the mean of the visible part of the spectrum.

**Answer:** 1. yellow light is scattered less by the fog particles

**Question 39. The pressure exerted by an electromagnetic wave of intensity I (watt / m2 ) on a non-reflecting surface is [c is the velocity of light]**

- I c
- I c2
- I / c
- I / c2

**Answer:** 3. I / c

**Question 40. An electromagnetic wave of frequency v = 3.0 MHz passes vacuum into a dielectric medium with permittivity ε = 4.0, then**

- The wavelength is doubled and the frequency remains unchanged
- Wavelength is doubled and frequency becomes half
- Wavelength is halved and frequency remains unchanged
- Wavelength and frequency both remain unchanged

**Answer:** 3. Wavelength is halved and frequency remains unchanged

**Question 41. The S.I unit of displacement current is**

- H
- A
- Fm
^{-1} - C

**Answer:** 2. A

**Question 42. The speed of electromagnetic waves is independent of**

- Wavelength
- Frequency
- Intensity
- Medium, in which it travels

**Answer:** 3. Intensity

**Question 43. Dimension of ε _{0}μ_{0}is :**

- LT
^{-1} - L
^{-1}T - L
^{2}T^{-2} - L–2 T
^{2}

**Answer:** 4. L^{-2} T^{2}

**Question 44. If ε _{0}and μ_{0}are the electric permittivity and magnetic permeability in free space, ε, and μ are the corresponding quantities in a medium, then the index of refraction of the medium is**

- \(\sqrt{\frac{\varepsilon_0 \mu}{\varepsilon \mu_0}}\)
- \(\sqrt{\frac{\varepsilon}{\varepsilon_0}}\)
- \(\sqrt{\frac{\varepsilon_0 \mu_0}{\varepsilon \mu}}\)
- \(\sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}}\)

**Answer:** 4. \(\sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}}\)

**Question 45. Red light differs from blue light while traveling in a vacuum is**

- Speed
- Frequency
- Intensity
- Amplitude

**Answer:** 2. Frequency

**Question 46. If an electromagnetic wave propagating through a vacuum is described by the following then E = E0sin (kx – ωt); B = B0sin (kx – ωt)**

- E0k = B0 ω
- E0B0= ω k
- E0 ω=B0k
- E0 B0= ω / k

**Answer:** 1. E0k = B0 ω

**Question 47. Which of the following is independent of wavelength? (k = propagation contact, ω = angular frequency)**

- k
- ω
- ωk
- k / ω

**Answer:** 4. k / ω

**Question 48. A magnetic field can be produced by**

- A charge at rest only
- A moving charge only
- Time-varying electric field
- Both by (2) and (3)

**Answer:** 4. Both by (2) and (3)

**Question 49. An electric charge in uniform motion produces**

- An electric field only
- A magnetic field only.
- Both electric and magnetic field
- No such field at all.

**Answer:** 3. Both electric and magnetic field

**Question 50. Which of the following radiation forms the part of electromagnetic spectrum**

- Alpha rays
- Beta rays
- Cathode rays
- Gamma rays

**Answer:** 4. Gamma rays

**Question 51. The oscillating electric and magnetic field vectors of electromagnetic waves are oriented along**

- The same direction and phase
- The same direction but have a phase difference of 90º
- Mutually perpendicular direction and are in phase
- Mutually perpendicular directions but has a phase difference of 90º

**Answer:** 3. Mutually perpendicular direction and are in phase

**Question 52. Which one of the following electromagnetic radiations has the smallest wavelength?**

- Ultraviolet waves
- X-rays
- γ-rays
- Microwaves

**Answer:** 3. γ-rays

**Question 53. Which of the following rays has minimum frequency?**

- U.V-rays
- X-rays
- Microwaves
- Infra-red-rays

**Answer:** 3. Microwaves

**Question 54. An accelerated electron would produce**

- γ-rays
- β-rays
- α-rays
- e.m. rays

**Answer:** 4. e.m. rays

**Question 55. The ozone layer blocks the radiation of wavelength :**

- Less than 3 × 10
^{-7}m. - Equal to 3 × 10
^{-7}m. - More than 3 × 10
^{-7}m. - None of these.

**Answer:** 1. Less than 3 × 10^{-7} m.

**Question 56. The frequencies of X-rays, γ-rays, and ultraviolet rays are respectively a, b, and c. Then**

- a < b, b > c
- a > b, b > c
- a > b, b < c
- a < b, b < c.

**Answer:** 1. a < b, b > c

**Question 57. When light travels from air to water, which parameter does not change?**

- Wavelength
- Frequency
- Velocity
- All of these

**Answer:** 2. Frequency

**Question 58. The velocity of light in a vacuum can be changed by changing**

- Frequency
- Amplitude
- Wavelength
- None of these.

**Answer:** 4. None of these.

**Question 59. Which of the following statements is wrong**

- Ultra-violet rays have a wavelength longer than infrared rays.
- Infrared rays travel with the same velocity as visible light.
- Infra-red can be focussed by a lens and can be reflected by a mirror just as visible light
- Infra-red rays have more heating power than visible light rays

**Answer: **1. Ultra-violet rays have a wavelength longer than infrared rays.

**Question 60. In an electromagnetic wave, the electric and magnetic fields are 100 Vm ^{-1} and 0.265 Am^{-1}. The maximum energy flow is**

- 26.5W/m
^{2} - 36.5W/m
^{2} - 46.7 Wm
^{2} - 765 W/m
^{2}

**Answer:** 1. 26.5W/m^{2}

**Question 61. In an apparatus, the electric field was found to oscillate with an amplitude of 18 V/m. The magnitude of the oscillating magnetic field will be**

- 4 × 10
^{-6}T - 6 × 10
^{-8}T - 9 × 10
^{-9}T - 11 × 10
^{-11}T

**Answer:** 2. 6 × 10^{-8} T

**Question 62. If a source is transmitting electromagnetic wave of frequency 8.2 × 10 ^{6} Hz, then the wavelength of the electromagnetic waves transmitted from the source will be**

- 36.6 m
- 40.5 m
- 42.3 m
- 50.9 m

**Answer:** 1. 36.6 m

**Question 63. There are three wavelengths 107 m, 10 ^{-10} m, and 10^{-7} m. Find their respective names**

- Radiowaves, X-rays, visible rays
- X-rays, Visible rays, Radio waves
- X-rays, γ-rays, Visible rays
- Visible rays, γ-rays, X-rays

**Answer:** 1. Radiowaves, X-rays, visible rays

**Question 64. Which of the following has the minimum frequency?**

- Radio wave
- Microwave
- Audible wave
- Ultrasonic wave

**Answer:** 3. Audible wave

**Question 65. Electromagnetic radiation of the highest frequency is**

- Infrared radiations
- Visible radiations
- Radiowaves
- γ-rays

**Answer:** 4. γ-rays

**Question 66. Which is having minimum wavelength :**

- X-rays
- Ultraviolet rays
- γ-rays
- Cosmic rays

**Answer:** 4. Cosmic rays

**Question 67. The range of wavelength of visible light is**

- 10 Å to 100 Å
- 4000 Å to 8000 Å
- 8000 Å to 10,000 Å
- 10,000 Å to 15, 000 Å

**Answer:** 2. 4000 Å to 8000 Å

**Question 68. The fact that radio signals reach the Earth from outside the atmosphere, was discovered by**

- K.G. Jansky
- Millikan
- Aryabhatta
- Prof. Kanu

**Answer:** 1. K.G. Jansky

**Question 69. Which of the following statements is true?**

- The velocity of light is constant in all media
- The velocity of light in a vacuum is the maximum
- The velocity of light is the same in all reference frames
- Laws of nature have identical forms in all reference frames

**Answer:** 2. The velocity of light in a vacuum is the maximum

**Question 70. The ozone layer absorbs**

- Infrared radiations
- Ultraviolet radiations
- X-rays
- γ-rays

**Answer:** 2. Ultraviolet radiations

**Question 71. A microwave and an ultrasonic sound wave have the same wavelength. Their frequencies are in the ratio (approximately)**

- 106: 1
- 104: 1
- 102: 1
- 10: 1

**Answer:** 1. 106: 1

**Question 72. Electromagnetic waves travel with a velocity**

- Equal to the velocity of light
- Equal to the velocity of sound
- Less than the velocity of light
- None of these

**Answer:** 1. Equal to the velocity of light

**Question 73. A capacitor has a capacity of 2pF. The electric field across the capacitor is changing with a value of 10 ^{12 }V/s. The displacement current is**

- 2 A
- 3 A
- 6 A
- 9 A

**Answer:** 1. 2 A

**Question 74. In a certain region of space electric field and magnetic field are bare perpendicular to each other, and an electron enters in region perpendicular to the direction of and Eboth moves undeflected, The velocity of the electron is:**

- \(\frac{|\vec{E}|}{|\vec{B}|}\)
- \(\vec{E} \times \vec{B}\)
- \(\frac{|\vec{B}|}{|\vec{E}|}\)
- \(\vec{E} \cdot \vec{B}\)

**Answer:** 1. \(\frac{|\vec{E}|}{|\vec{B}|}\)

**Question 75. What is the cause of the “Greenhouse effect”?**

- Infrared rays
- Ultraviolet rays
- X-rays
- Radiowaves

**Answer:** 1. Infrared rays

**Question 76. The velocity of electromagnetic waves is parallel**

- \(\vec{B} \times \vec{E}\)
- \(\vec{E} \times \vec{B}\)
- \(\vec{E}\)
- \(\vec{B}\)

**Answer:** 2. \(\vec{E} \times \vec{B}\)

**Question 77. Which of the following rays are not electromagnetic waves?**

- X-rays
- γ-rays
- β-rays
- Heat rays

**Answer:** 3. β-rays

**Question 78. Which of the following waves has the maximum wavelength?**

- X-rays
- I.R. rays
- UV rays
- Radiowaves

**Answer: **4. Radiowaves

**Question 79. Infrared radiation is detected by**

- Spectrometer
- Pyrometer
- Nanometer
- Photometer

**Answer:** 2. Pyrometer

**Question 80. Dimensions of\(\frac{1}{\mu_0 \in_0}\), where symbols have their usual meanings, are**

- [L
^{-1}T] - [L
^{-2}T^{2}] - [L
^{2}T–2] - [L T
^{-1}]

**Answer:** 3. [L^{2} T^{-2}]

**Question 81. Which of the following radiation has the least wavelength?**

- γ-rays
- β-rays
- α-rays
- X-rays

**Answer:** 1. γ-rays

**Question 82. Which of the following required no medium for propagation?**

- Cathode rays
- Electromagnetic rays
- Sound waves
- None of these

**Answer:** 2. Electromagnetic rays

## Electromagnetic Waves Exercise – 2

**Question 1. A uniform but time-varying magnetic field B (t) exists in a circular region of radius a it is directed into the plane of the paper as shown. The magnitude of the induced electric field at point P at a distance r from the center of the circular region.**

- Is zero
- Decreases as 1/r
- Increases as r
- Decreases as 1/r2

**Answer:** 2.

- Decreases as 1/r

**Question 2. Out of the following statement which is Not true?**

- Infrared radiations arise due to minor electron transitions in lighter atoms
- Infrared radiations are used for long-distance photography
- Sun is the only natural source of infrared radiation
- Infrared radiations are detected by using a spectrometer

**Answer: **4. Infrared radiations are detected by using a spectrometer

**Question 3. Which of the following has minimum wavelength?**

- X-rays
- Ultraviolet rays
- γ–rays
- Cosmic rays

**Answer: **4. Cosmic rays

**Question 4. If a light wave passes through a transparent medium (like glass). Then :**

- The velocity of all light waves will be the same
- Velocity of longer wavelength will be less
- The velocity of the longest wavelength will be the maximum
- The velocity of shorter wavelength will be the maximum

**Answer: **3. The velocity of the longest wavelength will be the maximum

**Question 5. The velocity of all radio waves in free space is 3 × 10 ^{8} m/s. The frequency of a radio wave of wavelength 150 m is :**

- 50 kHz
- 2 kHz
- 2 MHz
- 1 MHz

**Answer: **3. 2 MHz

**Question 6. Light waves travel in a vacuum along the y-axis. Which of the following may represent the wavefront?**

- y = constant
- x = constant
- z = constant
- x + y + z = constant

**Answer: **1. y = constant

**Question 7. Which of these statement is false :**

- A photographic plate is sensitive to infrared rays
- Photographic plates are sensitive to ultraviolet rays.
- Infrared rays are invisible but make shadow-like visible light
- As compared to visible light photons, infrared photon has more energy.

**Answer: **4. As compared to visible light photons, infrared photon has more energy.

**Question 8. The Eand Bvectors associated with an electromagnetic wave are :**

- Parallel to each other and are in the same phase
- Parallel to each other and are opposite in phase
- Perpendicular to each other and are opposite in phase
- Perpendicular to each other and are in phase

**Answer: **4. Perpendicular to each other and are in phase

**Question 9. The electric vector of an electromagnetic wave in a vacuum is represented by ˆ E 6.3jV / m =. The frequency of the wave is 20 MHz and it is propagating along the positive z-direction. At this point magnetic vector is**

- 2.1 × 10
^{-8}ˆiT - +2.1 × 10
^{-8}ˆiT - + 4.0 × 10
^{-8}ˆiT - –18.9 × 10
^{-8}ˆiT

**Answer: **1.2.1 × 10^{-8} ˆiT

**Question 10. Electromagnetic radiation of frequency ν, wavelength λ, traveling with velocity c in air, enters a glass slab of refractive index μ. The frequency, wavelength, and velocity of light in the glass slab will be respectively :**

- \(\frac{v}{\mu}, \frac{\lambda}{\mu} and \frac{\mathrm{c}}{\mu}\)
- \(v, \frac{\lambda}{\mu} and \frac{\mathrm{C}}{\mu}\)
- \(v, \mu \lambda and \frac{C}{\mu}\)
- \(\frac{v}{\mu}, \frac{\lambda}{\mu} and c\)

**Answer: **2. \(v, \frac{\lambda}{\mu} and \frac{\mathrm{C}}{\mu}\)

## Electromagnetic Waves Exercise – 3

**Question 1. The electric field of an electromagnetic wave in a medium is represented by Ex= 0 ;**

**\(E_y=2.5 \frac{\mathrm{N}}{\mathrm{C}} \cos \left[\left(2 \pi \times 10^6 \frac{\mathrm{rad}}{\mathrm{s}}\right) \mathrm{t}-\left(\pi \times 10^{-2} \frac{\mathrm{rad}}{\mathrm{m}}\right) \mathrm{x}\right]\)**

**Ez= 0. The wave is :**

- Moving along y direction with frequency 2π × 10
^{6}Hz and wavelength 200 m. - Moving along x direction with frequency 10
^{6}Hz and wavelength 100m - Moving along x direction with frequency 10
^{6}Hz and wavelength 200m - Moving along –x direction with frequency 10
^{6}Hz and wavelength 200m

**Answer:** 3. Moving along x direction with frequency 10^{6} Hz and wavelength 200m

**Question 2. Which of the following statements is false for the properties of electromagnetic waves?**

- Both electric and magnetic field vectors attain the maxima minima at the same place and same time.
- The energy in electromagnewaveswave is divided equally between electric and magnetic vectors.
- Both electric and magnetic field vectors are parallel to each other perpendicular to the direction of propagation of the wave.
- These waves do not require any material medium for propagation.

**Answer:** 3. Both electric and magnetic field vectors are parallel to each other perpendicular to the direction of propagation of wave.

**Question 3. The electric field of an electromagnetic wave in free space is given by E =10cos(10 t kx)j 7 ˆ+V/m, where t and x are in seconds and meters respectively. It can be inferred that**

- The wavelength λ is 188.4 m.
- The wave number k is 0.33 rad/m
- The wave amplitude is 10 V/m
- The wave is propagating the ong the +x direction

**Which one of the following pairs of statements is correct?**

- (3) and (4)
- (1) and (2)
- (2) and (3)
- (1) and (3)

**Answer:** 4. (1) and (3)

**Question 4. The electric field associated with an e.m. wave in vacuum is given by E I 40cos =(kz – 6 ×10 ^{8} t), where E, z, and t are in volt/m, meter, and seconds respectively. The value of wave vector k is :**

- 2 m
^{-1} - 0.5 m
^{-1} - 6 m
^{-1} - 3 m
^{-1}

**Answer:** 1. 2 m^{-1}

**Question 5. The ratio of the magnetic field to the amplitude electric field for an electromagnetic wave propagating in a vacuum is equal to the:**

- The speed of light in a vacuum
- Reciprocal of the speed of light in vacuum
- The ratio of magnetic permeability to the electric susceptibility of vacuum
- Unity

**Answer:** 2. Reciprocalthe of the speed of light in a vacuum

**Question 6. The condition under which a microwave oven he up food items containing water molecules most efficiently is :**

- The frequency of the microwaves has no relation with the natural frequency of water molecules.
- Microwaves are heat waves, so always produce heating.
- Infra-red waves produce heating in a microwave oven.
- The frequency of the microwaves must match the resonant frequency of the water molecules.

**Answer:** 4. The frequency of the microwaves must match the resonant frequency of the water molecules.

**Question 7. Out of the following options which one can be used to produce a propagating electromagnetic wave?**

- An accelerating charge
- A charge moving at constant velocity
- A stationary charge
- A chargeless particle

**Answer:** 1. An accelerating charge

**Question 8. In an electromagnetic wave in free s, pace the root mean square value of the electric field is Erms = 6V/m. The peak value of the magnetic field is :**

- 1.41 ×10
^{-8}T - 2.83 ×10
^{-8}T - 0.70 ×10
^{-8}T - 4.23 ×10
^{-8}T

**Answer:** 2. 2.83 ×10^{-8} T

**Question 9. An em wave is propagating in a medium with a velocity V =Vi. The instantaneous oscillating electric field of this em wave is the olong+y axis. Then the direction of the oscillating magnetic field of the em wave will be along**

- – z-direction
- – x direction
- – y direction
- + z direction

**Answer: **4. + z direction

**Question 10. Whcolorlour of the light has the longest wavelength?**

- Violet
- Red
- Blue
- Green

**Answer:** 2. Red

**Question 11. A parallel plate capacitor of capacitance 20 µF is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:**

- Zero, zero
- Zero, 60 µA
- 60 µA, 60 µA
- 60 µA, zero

**Answer:** 3. 60 µA, 60 µA

**Question 12. For a transparent medium, relative permeability and permittivity, μr, and ∈r are 1.0 and 1.44 respectively. The velocity of light in this medium would be :**

- 2.5 × 10
^{8} - 3 × 10
^{8} - 2.08 × 10
^{8}m/s - 4.32 × 10
^{8}m/s

**Answer:** 1. 2.5 × 10^{8}

**Question 13. The E.M. wave with the ith shortest wavelength among the following is**

- Ultraviolet rays
- X-rays
- Gamma-rays
- Microwaves

**Answer:** 1. Ultraviolet rays

**Question 14. The magnetic field in a plane electromagnetic wave is given by :\(\mathrm{B}_{\mathrm{y}}=2 \times 10^{-7} \sin \left(\pi \times 10^3 \mathrm{x}+3 \pi \times 10^{11} \mathrm{t}\right) \mathrm{T}\). Calculate the wavelength.**

- π× 10
^{3}m - 2 × 10
^{-3}m - 2 × 10
^{3}m - π× 10
^{-3}m

**Answer:** 2. 2 × 10^{-3} m

**Question 15. The ratio of contributions made by the electric field and magnetic field components to the intensity electromagnetic wave saves is : (c= speed of electromagnetic wave)**

- 1: 2
- c :1
- 1 :1
- 1: c

**Answer:** 3. 1: 1

**Question 16. For a plane electromagnetic wave propagating in the x-direction, which one of the following combinations gives the correct possible direction for the electric field I and magnetic field (2) respectively?**

- − j + k ,- j – k
- j + k ,- j – k
- -j + k ,- j + k
- j + k, j +k

**Answer:** 1. − j + k ,- j – k

**Question 17. An electromagnetic wave in a vacuum has the electric and magnetic fields E and B, which are always perpendicular to each other. The direction of polarization is given and X and that of wave propagation by k. Then**

- \(\vec{X} \| \vec{B} and \vec{k} \| \vec{B} \times \vec{E}\)
- \(\vec{X} \| \vec{E} and \vec{k} \| \vec{E} \times \vec{B}\)
- \(\overrightarrow{\mathrm{X}} \| \overrightarrow{\mathrm{B}} and \vec{k} \| \overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}}\)
- \(\overrightarrow{\mathrm{X}} \| \overrightarrow{\mathrm{E}} and \vec{k} \| \vec{B} \times \vec{E}\)

**Answer:** 2. \(\vec{X} \| \vec{E} and \vec{k} \| \vec{E} \times \vec{B}\)

**Question 18. The magnetic field traveling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is :**

- 3 V/m
- 6 V/m
- 9 V/m
- 12 V/m

**Answer:** 2. 6 V/m

**Question 19. During the propagation of electromagnetic waves in a medium :**

- Electric energy density is double the magnetic energy density.
- Electric energy density is half of the magnetic energy density.
- Electric energy density is equal to the magnetic energy density.
- Both electric and magnetic energy densities are zero.

**Answer:** 3. Electric energy density is equal to the magnetic energy density.

**Question 20. Match List-1 (Electromagnetic wave type) with List-2 (Its association/application) and select the correct option from the choices given below the lists :**

- (4) (3) (2) (1)
- (1) (2) (1) (3)
- (3) (2) (1) (4)
- (1) (2) (3) (4)

**Answer:** 4. (1) (2) (3) (4)

**Question 21. A red LED emits light at 0.1 watts uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is :**

- 1.73 V/m
- 2.45 V/m
- 5.48 V/m
- 7.75 V/m

**Answer:** 2. 2.45 V/m

**Question 22. Arrange the following electromagnetic radiations per quantum in the order of increasing energy :**

**A:** Blue light

**B:** Yellow light

**C:** X-ray

**D:** Radiowave

- A, B, D, C
- C, A, B, D
- B, A, D, C
- D, B, A, C

**Answer:** 4. D, B, A, C

**Question 23. An EM wave from the air enters a medium. The electric fields are \(\overrightarrow{\mathrm{E}}_1=\mathrm{E}_{01} \hat{x} \cos \left[2 \pi v\left(\frac{z}{c}-\mathrm{t}\right)\right]\) in air and \(\overrightarrow{\mathrm{E}}_2=\mathrm{E}_{02} \hat{x} \cos [\mathrm{k}(2 z-\mathrm{ct})]\)medium, where the wave number k and frequency υ refer to their values in air. The medium is non-magnetic. If εand r 1 εrefer to relative permittivities of air and medium r 2 respectively, which of the following options is correct **

- \(\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}}=\frac{1}{4}\)
- \(\frac{\varepsilon_{r_1}}{\varepsilon_{\mathrm{r}_2}}=\frac{1}{2}\)
- \(\frac{\varepsilon_{r_1}}{\varepsilon_{\mathrm{r}_2}}=4\)
- \(\frac{\varepsilon_{\mathrm{r}_1}}{\varepsilon_{\mathrm{r}_2}}=2\)

**Answer:** 1. \(\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}}=\frac{1}{4}\)

**Question 24. The energy associated with the electric field is (UE) and with magnetic field is (UB) for an electromagnetic wave in free space. Then :**

- UE < UB
- \(U_E=\frac{U_B}{2}\)
- UE > UB
- UE = UB

**Answer:** 4. UE = UB

**Question 25. If the magnetic field of a plane electromagnetic wave is given by (The speed of light =3 × 10 ^{8}m/s) B=100 × 10^{-6} sin \(\left[2 \pi \times 2 \times 10^{15}\left(t-\frac{x}{c}\right)\right]\) then the maximum electric field associated with it is**

- 4.5× 10
^{4}N/C - 4× 10
^{4}N/C - 6× 10
^{4}N/C - 3 × 10
^{4}N/C

**Answer:** 4. 3 × 10^{4} N/C

**Question 26. amplitude-modulated signal is given by V(t) = 10 [1+ 0.3 cos (2.2 × 10 ^{4}t) sin (5.5 × 10^{5}t)]. Hitre t is in seconds. The sideband frequencies (in kHz) are, [Given π = 22/7]**

- 892.5 and 857.5
- 89.25 and 85.75
- 1785 and 1715
- 178.5 and 171.5

**Answer:** 2. 89.25 and 85.75

**Question 27. An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index ‘n’ without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic field of the wave before and after entering into the medium are respectively, given by :**

- \((\sqrt{n}, \sqrt{n})\)
- \(\left(\frac{1}{\sqrt{n}}, \sqrt{n}\right)\)
- \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\)
- \(\left(\frac{1}{\sqrt{n}}, \frac{1}{\sqrt{n}}\right)\)

**Answer:** 3. \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\)

**Question 28. The displacement current flows in the dielectric of a capacitor when the potential difference across its plate**

- Is increasing with time
- Is decreasing with time
- Has assumed a constant value
- Becomes zero

**Answer:** 2. Is decreasing with time

**Question 29. The infrared spectrum lies between**

- Radio wave and microwave region.
- Microwave and visible region.
- Visible and ultra-violet region.
- Ultra-violet and X-ray.

**Answer:** 2. Microwave and visible region.

**Question 30. A man can take pictures of those objects which are not fully visible using camera films acceptable to**

- Ultraviolet rays
- Sodium light
- Visible light
- Infrared rays

**Answer:** 4. Infrared rays

**Question 31. The electromagnetic radiations are in descending order of wavelength in the following sequence**

- Infrared waves, radio waves, X–rays, visible light rays
- Radio– waves, infrared waves, visible light, X–rays
- Radio waves, visible light, infrared waves, X–rays
- X–rays, visible light, infrared waves, radio waves

**Answer:** 2. Radio– -waves, infra-red waves, visible light, X–rays

**Question 32. Maxwell’s describes the fundamental laws of**

- Electricity only
- Magnetism only
- Mechanics only
- Both (1) and (2)

**Answer:** 4. Both (1) and (2)

**Question 33. Heat radiations propagate at the speed of**

- α-rays
- β-rays
- Light waves
- Sound waves

**Answer:** 3. Light waves

**Question 34. Radio waves diffract around buildings although light waves do not. The reason is that radio waves :**

- Travel was with a speed larger than c
- Have a much larger wavelength than light
- Carry news
- Are not electromagnetic waves.

**Answer:** 2. Have a much larger wavelength than light

**Question 35. The curve drawn between the velocity and frequency of a photon in a vacuum will be**

- Straight line parallel to the frequency axis
- Straight line parallel to velocity axis.
- A straight line passing through the origin and making an angle of 45º with a frequency axis
- Hyperbola.

**Answer:** 1. Straight line parallel to the frequency axis

**Question 36. Which rays are not the portion of the electromagnetic spectrum?**

- X-rays
- Microwaves
- α-rays
- Radiowaves.

**Answer:** 3. α-rays

**Question 37. The difference between soft and hard X-rays is of**

- Velocity
- Intensity
- Frequency
- Polarization

**Answer:** 3. Frequency