The electric field of an electromagnetic wave in free space is represented as → E = E _ 0 ( - kz ) ^ i . The corresponding magnetic induction vector will be :

Correct answer: B. → B = E _ 0 C ( - kz ) ^ j Given → E = E _ 0 ( - kz ) ^ i : Clearly, ( - kz ) term represents, electromagnetic wave is travelling along + z direction or along ^ k . Now, in vector form, direction of electromagnetive wave is given by ^ C = ^ E × ^ B . Therefore, magnetic field is along ^ j . Also, we know that B _ 0 = E _ 0 C , where C is speed of light. Therefore, → B = E _ 0 C ( - kz ) ^ j .

JEE Main 202430 JanuaryMorning Shift

Exam: JEE Main
Year: 2024
Date: 30 January
Shift: Morning Shift
Subject: Physics
Chapter: Electromagnetic Waves

JEE Main 2024 · 30 January · Morning Shift · Physics · Electromagnetic Waves

The electric field of an electromagnetic wave in free space is...

The electric field of an electromagnetic wave in free space is represented as

\overset{\to}{E} = {E}_{0}\cos ( \omegat - kz ) \overset{^}{i}

. The corresponding magnetic induction vector will be :

Options

A $\overset{\to}{B} = {E}_{0}Ccos ( \omegat - kz ) \overset{^}{j}$
B $\overset{\to}{B} = \dfrac{{E}_{0}}{C}\cos ( \omegat - kz ) \overset{^}{j}$
C $\overset{\to}{B} = {E}_{0}Ccos ( \omegat + kz ) \overset{^}{j}$
D $\overset{\to}{B} = \dfrac{{E}_{0}}{C}\cos ( \omegat + kz ) \overset{^}{j}$

Correct answer

B. $\overset{\to}{B} = \dfrac{{E}_{0}}{C}\cos ( \omegat - kz ) \overset{^}{j}$

Step-by-step solution

Given $\overset{\to}{E} = {E}_{0}\cos ( \omegat - kz ) \overset{^}{i}$ :

Clearly, $( \omegat - kz )$ term represents, electromagnetic wave is travelling along $+ z$ direction or along $\overset{^}{k}$ .

Now, in vector form, direction of electromagnetive wave is given by $\overset{^}{C} = \overset{^}{E} \times \overset{^}{B}$ . Therefore, magnetic field is along $\overset{^}{j}$ .

Also, we know that ${B}_{0} = \dfrac{{E}_{0}}{C}$ , where $C$ is speed of light.

Therefore, $\overset{\to}{B} = \dfrac{{E}_{0}}{C}\cos ( \omegat - kz ) \overset{^}{j}$ .

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