Question 4

4 [35 points] The diagram below represents a "snapshot" of a linearly polarized light wave at an instant in time. The electric field, with amplitude Eo, points in the ± y direction; the magnetic field, with amplitude Bo, points in the ± z direction.

 

Two halves of a long conducting wire are connected to different terminals of a light bulb. This device is so that the wire is oriented in the x-y plane and tilted an angle a with respect to the y-axis, as shown. The bulb is observed to glow.

 
  1. [5 pts] What is the direction of propagation of the wave? Explain how you can tell.

    2. The wave propagates in the positive x direction, determined by the direction of the Poynting vector,

    E X B.

     

  2. [10 pts] For each of the following changes, state whether the brightness of the light bulb would increase, decrease, or remain the same. Explain your reasoning in each case.

The brightness of the bulb would remain the same. Charges accelerated in the wire produce a current which lights the bulb. The force on a charge due to the electric field is exerted in the same direction as the electric field and is proportional to the magnitude of the electric field. Since neither the direction nor magnitude of the electric field varies with y, moving the wire along the y axis does not change the amount of current flowing through the bulb.

 

 

The brightness of the bulb would decrease. As a increases, the component of E parallel to the wire decreases. Since the parallel component of E accelerates charges in the wire and produces current, there will be less current than in the original case, resulting in a dimmer bulb.

 
  1. [20 pts] The wire and bulb device is now removed and a polarizing filter is placed at x = 0 so that the light is incident normally on the filter. The direction of polarization of the filter is oriented so that it makes an angle of 30° with the y-axis.

• Give the direction and write an expression (in terms of E0) for the magnitude of the electric field of the transmitted wave. Explain.

 

Only the component of the electric field parallel to the direction of polarization will be transmitted.

Etrans = Eo cos(30° )= 0.866 Eo

• Give the direction and write an expression (in terms of B0) for the magnitude of the magnetic field of the transmitted wave. Explain.

Only the component of the magnetic field perpendicular to the direction of polarization will be transmitted.

Btrans = Bo cos(30° )= 0.866 Bo