Problem Set 3


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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 3 Due: Wednesday, February 27 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32- 082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1 (10 points): Concept Questions. Explain your reasoning. Concept Question 1: A pyramid has a square base of side a, and four faces which are equilateral triangles. A charge Q is placed on the center of the base of the pyramid. What is the net flux of electric field emerging from one of the triangular faces of the pyramid? 1. 0 2. 0 8 Q ε 3. 2 0 2 Qa 4. 0 2 Q 5. Undetermined: we must know whether Q is infinitesimally above or below the plane? Explain your reasoning: Concept Question 2: A charge distribution generates a radial electric field G E = a r 2 e r / b ˆ r where a and b are constants. The total charge giving rise to this electric field is 1. 0 4 a πε 2. 0 3. 0 4 b Explain your reasoning:
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Problem 2: (10 points) Non-uniformly charged sphere A sphere of radius R has a charge density 0 (/ ) rR ρ = where 0 is a constant and is the distance from the center of the sphere. r a) What is the total charge inside the sphere? b) Find the electric field everywhere (both inside and outside the sphere). c) Find the electric potential difference between the center of the sphere and a distance r away from the center for both r < R and r > R . Be sure to indicate where you have chosen your zero reference potential. d) How much energy does it take to assemble this charge distribution? Problem 3 (10 points) ( Thundercloud ): The bottom surface of a thundercloud of area A and the earth can be modeled as a pair of infinite parallel plate with equal and opposite surface uniform charge densities.
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This note was uploaded on 11/10/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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