A sinusoidal beam of electromagnetic radiation that is only 2 cm high propagates

Question

A sinusoidal beam of electromagnetic radiation that is only 2 cm high propagates in the +x direction, with the electric field in the +/-z direction. The beam strikes a metal rod that is centered on the origin and aligned along the z axis, as shown in the figure.

You place detectors sensitive to electromagnetic radiation at location 0,17,0 m (detector A) and location 0,0,17 m (detector B).

Answer the following questions for detector A and for detector B: Will the detector detect electromagnetic radiation? If so:

(a)What is the direction of propagation of the electromagnetic radiation detected?

(b)What is the direction of the electric field in the radiation?

(c)What is the direction of the magnetic field in the radiation?

Explanation / Answer

Since Detector A is at (0,17,0) and the electromagnetic waves are only confined to the xz-plane, therefore, this detector will detect no electromagnetic radiation.

For Detector B, the detector will detect electromagnetic radiation propagating in positive x direction. Its direction of electric field will be along +z direction.

Since the magnetic field, electric field and direction of propagation are mutually perpendicular, therefore, the magentic field detected by B will be directed along positive y axis.

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