©1997 by Eric Mazur Published by Pearson Prentice Hall Upper Saddle River, NJ 07458 ISBN 0-13-565441-6 No portion of the file may be distributed, transmitted in any form, or included in other documents without express written permission from the publisher.

Electrodynamics

1. constant electric field. 2. changing electric field. As the capacitor shown below is charged with a constant current I, at point P there is a 1. constant electric field. 2. changing electric field. 3. constant magnetic field. 4. changing magnetic field. 5. changing electric field and a magnetic field. 6. changing magnetic field and an electric field. 7. none of the above. Answer: 5. As the charge on the capacitor increases, the electric field increases. The changing electric field, in turn, generates a magnetic field.

For a charging capacitor, the total displacement current between the plates is equal to the total conduction current I in the wires. The capacitors in the diagram have circular plates of radius R. In (a), points A and B are each a distance d > R away from the line through the centers of the plates; in this case the magnetic field at A due to the conduction current is the same as that at B due to the displacement current. In (b), points P and Q are each a distance r < R away from the center line. Compared with the magnetic field at P, that at Q is 1. bigger. 2. smaller. 3. the same. 4. need more information. Answer: 2.The magnetic field at P is proportional to the entire conduction current, as can be seen by drawing an amperian loop of radius r through P. At Q, however, only a fraction r2/R2 of the changing electric flux, and hence of the displacement current, contributes to the magnetic field. Thus, the magnetic field at Q will be smaller than that at A.

A planar electromagnetic wave is propagating through space A planar electromagnetic wave is propagating through space. Its electric field vector is given by E = Eo cos(kz – wt) Its magnetic field vector is Answer: 1.From the expression for the electric field vector we see that the wave is propagating in the z direction with the electric field aligned along the x axis. Propagating electromagnetic waves have orthogonal electric and magnetic fields.

At a fixed point, P, the electric and magnetic field vectors in an electromagnetic wave oscillate at angular frequency w. At what angular frequency does the Poynting vector oscillate at that point? 1. 2w 2. w 3. w /2 4. 4w Answer: 1. The Poynting vector is proportional to the cross product of the electric and magnetic field vectors. Since both fields oscillate sinusoidally with frequency ω, trigonometric identities show that their product is a sinusoidal function of frequency 2ω.

1. a 50-W source at a distance R. 2. a 100-W source at a distance 2R. Which gives the largest average energy density at the distance specified and thus, at least qualitatively, the best illumination 1. a 50-W source at a distance R. 2. a 100-W source at a distance 2R. 3. a 200-W source at a distance 4R. Answer: 1. The energy density at the specified point is proportional to the power divided by the surface area of the indicated sphere.