Electromagnetic Waves — Page 3 | NEET Physics

Q21

The electric field associated with an em wave in vacuum is given by E =

\widehat i

40 cos (kz

-

6

\times

10 8 t) where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is

A 2 m

-

1

B 0.5 m

-

1

C 6 m

-

1

D 3 m

-

1

Correct Answer

Option A

Solution

Compare the given equation with E = E 0 cos(kz -

\omega t

) we get, $\omega$ = 6 $\times$ 10 8 s -1 Wave vector, k =

{\omega \over c}

=

{{6 \times {{10}^8}} \over {3 \times {{10}^8}}}

= 2 m -1

Q22

The electric and the magnetic field, associated with an e.m. wave, propagating along the +z-axis, can be represented by

A

\left[ {\overrightarrow E = {E_0}\widehat i,\overrightarrow B = {B_0}\widehat j} \right]

B

\left[ {\overrightarrow E = {E_0}\widehat k,\overrightarrow B = {B_0}\widehat i} \right]

C

\left[ {\overrightarrow E = {E_0}\widehat j,\overrightarrow B = {B_0}\widehat i} \right]

D

\left[ {\overrightarrow E = {E_0}\widehat j,\overrightarrow B = {B_0}\widehat k} \right]

Correct Answer

Option A

Solution

The e.m. wave is propagating along +z direction.

Electric field and magnetic field are mutually perpendicular and also perpendicular to the direction of propagation.

$\therefore$

\left[ {\overrightarrow E = {E_0}\widehat i,\overrightarrow B = {B_0}\widehat j} \right]

Q23

The decreasing order of wavelength of infrared, microwave, ultraviolet and gamma rays is

A microwave, infrared, ultraviolet, gamma rays

B gamma rays, ultraviolet, infraref, microwaves

C microwaves, gamma rays, infrared, ultraviolet

D infrared, microwave, ultraviolet, gamma rays

Correct Answer

Option A

Solution

From the electromagnetic wave spectrum, the correct decreasing order of wavelength is : microwave, infrared, ultraviolet, gamma rays.

Q24

The electric field of an electromagnetic wave in free space is given by

\overrightarrow E = 10\cos ({10^7}t + kx)\widehat j\,\,V/m,

where t and x are in seconds and metres respectively. It can be inferred that (1) the wavelength

\lambda

is 188.4 m. (2) the wave number k is 0.33 rad/m. (3) the wave amplitude is 10 V/m. (4) the wave is propagating along +x direction. Which one of the following pairs of statements is correct ?

A (3) and (4)

B (1) and (2)

C (2) and (3)

D (1) and (3)

Correct Answer

Option D

Solution

As given,

E = 10\cos ({10^7}t + kx)\widehat j\,\,V/m

here amplitude E 0 = 10 V/m and $\omega$ = 10 7 rad/s As c =

\nu \lambda = {{\omega \lambda } \over {2\pi }}

$\Rightarrow$ $\lambda$ =

{{2\pi c} \over \omega }

=

{{2\pi \times 3 \times {{10}^8}} \over {{{10}^7}}}

= 188.4 m Also, c =

{\omega \over k}

$\Rightarrow$ k =

{\omega \over c} = {{{{10}^7}} \over {3 \times {{10}^8}}}

= 0.033 The wave is propagating along y direction.

Q25

Which of the following statement is false for the properties of electromagnetic waves ?

A Both electric and magnetic field vectors attain the maxima and minima at the same place and same time.

B The energy in electromagnetic wave is divided equally between electric and magnetic vectors.

C Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave.

D These waves do not require any material medium for propagation.

Correct Answer

Option C

Solution

In an electromagnetic wave it is observed that electric and magnetic vectors are perpendicular to each other and are perpendicular to the direction of propagation of wave.

Q26

The electric field part of an electromagnetic wave in a medium is represented by E x = 0;

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

E z = 0.

A moving along x direction with frequency 10 6 Hz and wavelength 100 m.

B moving along x direction with frequency 10 6 Hz and wavelength 200 m.

C moving along

-

x direction with frequency 10 6 Hz and wavelength 200 m.

D moving along y direction with frequency

2\pi \times {10^6}\,Hz

and wavelength 200 m.

Correct Answer

Option B

Solution

Since coefficient of x is negative, but is moving along +ve x-axis, so This is the form E y = E 0 ( $\omega$ t – kx) $\omega$ =

{2\pi \times {{10}^6}}

f =

{\omega \over {2\pi }}

= 10 6 Hz k =

\pi \times {10^{ - 2}}

Also,

\lambda = {{2\pi } \over k}

=

{{2\pi } \over {\pi \times {{10}^{ - 2}}}}

= 200 m

Q27

The velocity of electromagnetic radiation in a medium of permittivity

\varepsilon

0 and permeability

\mu

0 is given by

A

{1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}

B

\sqrt {{{{\mu _0}} \over {{\varepsilon _0}}}}

C

\sqrt {{{{\varepsilon _0}} \over {{\mu _0}}}}

D

\sqrt {{\mu _0}{\varepsilon _0}}

Correct Answer

Option A

Solution

The velocity of electromagnetic radiation in vacuum is =

{1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}

Q28

The electric and magnetic field of an electromagnetic wave are

A in opposite phase and perpendicular to each other

B in opposite phase and parallel to each other

C in phase and perpendicular to each other

D in phase and parallel to each other.

Correct Answer

Option C

Solution

In electromagnetic waves, E and B are in same phase and perpendicular to each other.

Q29

If

\lambda

v ,

\lambda

x and

\lambda

m represent the wavelengths of visible light, X-rays and microwaves respectively, then

A

{\lambda _m} > {\lambda _x} > {\lambda _v}

B

{\lambda _m} > {\lambda _v} > {\lambda _x}

C

{\lambda _v} > {\lambda _x} > {\lambda _m}

D

{\lambda _v} > {\lambda _m} > {\lambda _x}

Correct Answer

Option B

Solution

{\lambda _m} > {\lambda _v} > {\lambda _x}

In spectrum X-rays has minimum wavelength and microwave has maximum wavelength.

Q30

Which of the following rays are not electromagnetic waves ?

A X-rays

B

\gamma

-rays

C

\beta

-rays

D heat rays

Correct Answer

Option C

Solution

Electromagnetic waves are a form of energy waves that have both an electric and magnetic field such as Radio Waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays.

So $\beta$ -rays are not electromagnetic waves, but it is a beam of fast electrons.