Expression for Electric Field - Electromagnetism and Optics - Exam, Exams of Electromagnetism and Electromagnetic Fields Theory

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Physics 1 10a Fall 2004 Prof. Orenstein Quiz #2: To help with grading, please either show your work or explain (briefly) your reasoning. Problem 1: 20 points Consider a sphere of total charge Q, suspended so that its center is 2) above a conducting plane. Find an expression for the electric field at the surface of the conductor in the limit that the distance from the sphere tends to infinity. Problem 2: 40 points The potential outside of a spherical shell of charge (radius 2) varies along the positive z- axis as: R Vou Z) = Vo Zz assuming that the origin of coordinates is the center of the sphere. (a) Find the potential everywhere outside of the shell. [25 points] (b) What is the direction of the electric field in the z=0 plane? (It may help to express cos@ as z/r) [15 points] Problem 3: 40 points The region between two concentric spherical shell conductors is filled with two kinds of dielectric material, as shown in the diagram below. The inner conductor has uniform surface charge o and its radius is a. The inner dielectric has permittivity ¢, and the outer has permitivity ¢). The interface lies halfway between the conductors. Find the bound charge at the interface.