PHYS 303 Final, Fall 1997

AUB Electrodynamics I Feb. 6, 1998 Physics Dept. Physics 303 Time 3 hours Problem 1. a) Using Maxwell’s Equations and Ohm’s law show that in a conductor of conductivity co and no net charge density ( p = 0 ), dno GE LCE 2 Ve E=—— oe ét & at b) Suppose that the conductor carries an alternating current J=f o eo 42010 —— J=0. o Show that if it’s a good conductor (a >> @ ), then V7 7+ ¢) Suppose that the conductor is a metal slab filling the space - d <x <d and that the current flows in the y-direction. Find the current distribution J (x, t) and plot it against x, given that on the surface of the metal slab (x = +d), the electric field is F=Ey &°™. §. Problem 2 Show that the self inductance of a toroidal solenoid of N turns can be given by: L=uN(R-(R’-r)?] in which r is the radius of the circular cross section of the solenoid, and R is the radius of the toroid. You may need the integral: (a> b> 0) l= * sin’ 8d@ 2% [a-(a- by] aatbcos@ be Problem 3 A very long dielectric cylinder of radius R and dielectric constant k is placed in a uniform electric field 9: The axis of the cylinder is oriented at right angles to the direction of the uniform electric field. The cylinder contains no free charges. Determine the electric field at points inside and outside the cylinder.