An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The direction of the polarization of the magnetic field associated with this wave is
A) $\hat { j }$

B) $\hat { k }$
C) $\hat { i }$
D) Hold on. The wave is not polarized.

Question

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The direction of the polarization of the magnetic field associated with this wave is
A) $\hat { j }$

B) $\hat { k }$
C) $\hat { i }$
D) Hold on. The wave is not polarized.

Quizplus · Accepted Answer

The direction of the magnetic field ($\vec{B}$) in an electromagnetic wave is perpendicular to the direction of the electric field ($\vec{E}$). Given $\vec{E}$ is in the $\hat{j}$ direction and the wave propagates in the $\hat{k}$ direction (implied by the term $kz$ in the phase of the cosine function), $\vec{B}$ must be perpendicular to both $\hat{j}$ and $\hat{k}$, which is in the $\hat{i}$ direction.

An Electromagnetic Wave Has an Electric Field Given By the Direction of the Polarization of the Magnetic Field