The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_{0} \cos (\omega t-k z) \hat{i}$. The corresponding magnetic induction vector will be :

(B) $\vec{B}=\frac{E_{0}}{C} \cos (\omega t-k z) \hat{j}$

(A) $\vec{B}=E_{0} C \cos (\omega t-k z) \hat{j}$

(C) $\vec{B}=E_{0} C \cos (\omega t+k z) \hat{j}$

(D) $\vec{B}=\frac{E_{0}}{C} \cos (\omega t+k z) \hat{j}$

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · EM Waves

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

E = E_{0} cos (ω t - k z) \hat{i}

.

The corresponding magnetic induction vector will be :

(A) $B = E_{0} C cos (ω t - k z) \hat{j}$
(B) $B = \frac{E _{0}}{C} cos (ω t - k z) \hat{j}$ ✓ Correct
(C) $B = E_{0} C cos (ω t + k z) \hat{j}$
(D) $B = \frac{E _{0}}{C} cos (ω t + k z) \hat{j}$

Answer: (B)

Solution

For a plane EM wave,

B_{0} = E_{0} / c

, and

\hat{k} = \hat{E} \times \hat{B}

. With

E

along

\hat{i}

and propagation along

+ z

B

must be along

\hat{j}

with the same phase:

B = \frac{E _{0}}{c} cos (ω t - k z) \hat{j}

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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