An electromagnetic wave travelling in the x - direction has...

An electromagnetic wave travelling in the

x -

direction has frequency of

2 \times {10}^{14}Hz

and electric field amplitude of

27V{m}^{– 1}

oscillates in

Y -

direction. From the options given below, which one describes the magnetic field for this wave?

Options

A\overset{\to}{B}\left(x, t\right) = ( 9 \times {10}^{- 8}T ) \overset{^}{j} \sin \left[1.5 \times {10}^{- 6}x - 2 \times {10}^{14}t\right]
B $\overset{\to}{B}\left(x, t\right) = ( 9 \times {10}^{- 8}T ) \overset{^}{i}\sin \left[2\pi\left(1.5 \times {10}^{- 8}x - 2 \times {10}^{14}t\right)\right]$
C $\overset{\to}{B}$ $\left(x, t\right) = \left(3 \times {10}^{- 8}T\right)\overset{^}{j}\sin 2 \pi\left[\left(\dfrac{x}{1.5 \times {10}^{- 8}}\right) - 2 \times {10}^{14}t\right]$
D $\overset{\to}{B}$ $\left(x, t\right) = \left(9 \times {10}^{- 8}T\right)\overset{\text{^}}{k}\sin 2 \pi\left[\left(\dfrac{x}{1.5 \times {10}^{- 6}}\right) - 2 \times {10}^{14}t\right]$

Correct answer

D. $\overset{\to}{B}$ $\left(x, t\right) = \left(9 \times {10}^{- 8}T\right)\overset{\text{^}}{k}\sin 2 \pi\left[\left(\dfrac{x}{1.5 \times {10}^{- 6}}\right) - 2 \times {10}^{14}t\right]$

Step-by-step solution

When undefined

Then

B = {B}_{0}sin

( kx - \omegat )

Of light in travelling along

\overset{^}{i} then

\overset{\to}{B}

in either along

\overset{^}{j}

or

\overset{^}{k}

.<br /><br />

∴

speed of light

C = \dfrac{{E}_{0}}{{B}_{0}} ⇒ {B}_{0} = \dfrac{{E}_{0}}{C}

<br /><br />

⇒ {B}_{0} = \dfrac{27}{3 \times {10}^{8}} = 9 \times {10}^{- 8}T

<br /><br />also,

\omega = 2\pif = 2\pi \times 2 \times {10}^{14} = 4\pi \times {10}^{14}

<br /><br />

k = \dfrac{\omega}{c} = \dfrac{4\pi \times {10}^{14}}{3 \times {10}^{8}}

<br /><br />

= ( \dfrac{2\pi}{1.5 \times {10}^{- 6}} )

<br /><br />Looking into the option the correct<br /><br />Answer is

\overset{\to}{B} = 9 \times {10}^{- 8}\sin 2\pi

\left(\dfrac{x}{1.5 \times {10}^{- 6}} - 2 \times {10}^{14}t\right)\overset{^}{k}

Practice Electromagnetic Waves on Quantrex Academy →

More from Electromagnetic Waves

The electric field associated with an electromagnetic wave travelling in vacuum is given… JEE Advanced 2026 A monochromatic source of light operating at 15 kW emits 2.5× 10^ 22 photons/s. The… JEE Main 2026 For an electromagnetic wave propagating through vacuum, k , E and ω represent propagation… JEE Main 2026 A point light source emits E.M. waves in free space. A detector, placed at a distance of… JEE Main 2026 A displacement current of 4.0 A can be set up in the space between two parallel plates of… JEE Main 2026 A magnetic field vector in an electromagnetic wave is represented by B =B_0 (2π vt-(2π… JEE Main 2026 An electromagnetic wave travels in free space along the x -direction. At a particular… JEE Main 2026 An electromagnetic wave travelling in x -direction is described by field equation E_y =… JEE Main 2026 Full Electromagnetic Waves list All JEE Main PYQs