The magnetic field of an E.M. wave is given by vec B = (frac √(3) 2 hat i +1/2 hat j ) 30 sin [ω ( t -frac z c ) ] (S.I. Units) The corresponding electric field in S.I. units is :

vec E = (1/2 hat i -frac √(3) 2 hat j ) 30 c sin [ω (t-z/c ) ]

overrightarrow E = (3/4 hat i +1/4 hat j ) 30 cos [ω ( t -frac z c ) ]

overrightarrow E = (1/2 hat i +frac √(3) 2 hat j ) 30 c sin [ω ( t +frac z c ) ]

overrightarrow E = (frac √(3) 2 hat i -1/2 hat j ) 30 c sin [ω ( t +frac z c ) ]

Physics · Electromagnetic Waves

JEE Main 2025 — 28 January, Evening Shift — Question 62

The magnetic field of an E.M. wave is given by $\vec{B}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{\mathrm{j}}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)\right]$ (S.I. Units) The corresponding electric field in S.I. units is :

Option A:
$\vec{E}=\left(\frac{1}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j}\right) 30 c \sin \left[\omega\left(t-\frac{z}{c}\right)\right]$
Correct
Option B:
$\overrightarrow{\mathrm{E}}=\left(\frac{3}{4} \hat{\mathrm{i}}+\frac{1}{4} \hat{\mathrm{j}}\right) 30 \cos \left[\omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)\right]$
Option C:
$\overrightarrow{\mathrm{E}}=\left(\frac{1}{2} \hat{\mathrm{i}}+\frac{\sqrt{3}}{2} \hat{\mathrm{j}}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{\mathrm{z}}{\mathrm{c}}\right)\right]$
Option D:
$\overrightarrow{\mathrm{E}}=\left(\frac{\sqrt{3}}{2} \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{\mathrm{z}}{\mathrm{c}}\right)\right]$

Answer: A

Step-by-step solution

$\quad \vec{B}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right) 30 \sin \left[\omega\left(t-\frac{z}{c}\right)\right]$

$\overrightarrow{\mathrm{E}}=\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{c}}$ and $\mathrm{E}=\mathrm{B}_{0} \mathrm{c}$

Here $\vec{E}\left(\frac{\sqrt{3}}{2}(-\hat{\mathrm{j}})+\frac{1}{2} \hat{\mathrm{i}}\right)$

$\mathrm{E}_{0}=30 \mathrm{c}$

$\vec{E}=\left(\frac{1}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j}\right) 30 c \sin \left[\omega\left(t-\frac{z}{c}\right)\right]$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Evening Shift
Subject: Physics
Chapter: Electromagnetic Waves
Topic: Displacement Current and Equation of EM Waves