The magnetic field in a plane electromagnetic wave is given by B = B0 sin(kx + omega t) k-hat. What is the expression for the electric field vector?

B. -c B_0 (kx + t) j — The wave propagates in the negative x-direction because of the (kx + omega t) term. The direction of propagation is given by the cross product of E and B. Since the wave travels in -i and B is in k, E must be in -j.

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$The magnetic field in a plane electromagnetic wave is given by B = B_{0} sin (k x + ω t) \hat{k} . What is the expression for the electric field vector E ?$

A. $c B_{0} sin (k x + ω t) \hat{j}$
B. $- c B_{0} sin (k x + ω t) \hat{j}$
C. $c B_{0} sin (k x + ω t) \hat{i}$
D. $- c B_{0} sin (k x + ω t) \hat{i}$

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Correct answer: B — $- c B_{0} sin (k x + ω t) \hat{j}$

Solution

Direction of propagation is - \hat{i} . Since S \propto E \times B, we have - \hat{i} = \hat{E} \times \hat{k} . This implies \hat{E} = - \hat{j} . Thus E = - c B_{0} sin (k x + ω t) \hat{j} .

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The magnetic field in a plane electromagnetic wave is given by B=B0​sin(kx+ωt)k^. What is the expression for the electric field vector E?

Solution

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More Electromagnetic Waves practice questions

$The magnetic field in a plane electromagnetic wave is given by B = B_{0} sin (k x + ω t) \hat{k} . What is the expression for the electric field vector E ?$