Tessellate S.T.E.M.S - Physics - College - Set 2 - Problem 1

Electricity and Magnetism Level 3

Which of the following pairs of electric and magnetic field correspond to fields in free space?

( a ) (a) E = x ^ E 0 cos ⁡ ( ω t − k x ) , = \hat{x}E_0 \cos(\omega t - k x), \hspace{0.5cm} B = − y ^ k E 0 ω cos ⁡ ( ω t − k x ) = - \hat{y}\frac{k E_0}{\omega} \cos(\omega t - k x)

( b ) (b) E = x ^ E 0 cos ⁡ ( ω t − k y ) , = \hat{x}E_0 \cos(\omega t - k y), \hspace{0.5cm} B = − z ^ k E 0 ω cos ⁡ ( ω t − k y ) = - \hat{z}\frac{k E_0}{\omega} \cos(\omega t - k y)

( c ) (c) E = x ^ E 0 cos ⁡ ( ω t − k y ) , = \hat{x}E_0 \cos(\omega t - k y), \hspace{0.5cm} B = z ^ k E 0 ω cos ⁡ ( ω t − k y ) = \hat{z}\frac{k E_0}{\omega} \cos(\omega t - k y)

( d ) (d) E = x ^ E 0 cos ⁡ ( ω t − k x ) , = \hat{x}E_0 \cos(\omega t - k x), \hspace{0.5cm} B = y ^ k E 0 ω cos ⁡ ( ω t − k x ) = \hat{y}\frac{k E_0}{\omega} \cos(\omega t - k x)

This problem is a part of Tessellate S.T.E.M.S.

d a c b

Writabrata Bhattacharya by Writabrata Bhattacharya , 22, India

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1 solution

Steven Chase
Jan 4, 2018

Thought process:

1) Looking at the trig function arguments, these are forward-propagating waves, traveling along the axis indicated in the trig function arguments. They are forward-propagating because as time increases, the position must increase to keep the argument the same (as if we were following a particular point on the wave).

2) The E and B fields must be perpendicular to the propagation direction. This rules out (a) and (d).

3) (b) and (c) are almost identical. Therefore, invoke the Poynting Vector. Assuming that the energy propagates in the same direction as the wave, the cross product of E and B (E cross B) must be in the +y direction. Using the right-hand rule, we see that (b) is the only viable answer.

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