A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) E =9.6 j V / m. The value of magnetic field at this point is _______.

(B) 3.2 \times 10^{-8}\ \hat{\mathrm{i}}

(C) 9.6 \ \hat{\mathrm{j}} \mathrm{T}

(D) 9.6 \times 10^{-8}\ \hat{\mathrm{kT}}

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JEE Mains · Physics · STD 12 - Electromagnetic waves

JEE Mains 2024
Hard
MCQ

A plane electromagnetic wave of frequency \(35\ \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\ \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______.

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(A) \(3.2 \times 10^{-8} \ \hat{\mathrm{k}} \mathrm{T}\)

Step-by-step Solution

Detailed explanation

\( \frac{E}{B}=C \)

\( \frac{E}{B}=3 \times 10^8\)

\(B =\frac{E}{3 \times 10^8}=\frac{9.6}{3 \times 10^8} \)

\(B =3.2 \times 10^{-8} \mathrm{~T} \)

\(\hat{B} =\hat{v} \times \hat{E} \)

\( =\hat{i} \times \hat{j}=\hat{k}\)

So,

\(\overrightarrow{\mathrm{B}}=3.2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}\)

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