An electromagnetic wave is propagating in a vacuum with an electric field given by E = E0 sin(kx - omega*t) j-cap. What is the direction of the associated magnetic field B?

A. k — The direction of propagation is given by the cross product of the electric and magnetic fields, specifically the direction of the Poynting vector is E cross B. Since the wave propagates in the x-direction and E is in the y-direction, B must be in the z-direction to satisfy the cross product relation.

JEE Main · PhysicsMedium

$An electromagnetic wave is propagating in a vacuum with an electric field given by $\vec{E} = E_0 \sin(kx - \omega t) \hat{j}$. What is the direction of the associated magnetic field $\vec{B}$?$

A. $\hat{k}$
B. $-\hat{k}$
C. $\hat{i}$
D. $-\hat{j}$

Show correct answer & step-by-step solution

Correct answer: A — $\hat{k}$

Solution

The direction of propagation is given by

S \propto E \times B

. Given

E = E_{0} \hat{j}

and propagation direction

\hat{i}

, we have

\hat{i} = \hat{j} \times B

, which implies

B

must be in the

\hat{k}

direction.

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