Electricity and Magnetism I (P331) Homework 3 Due: Wednesday, September 23, 4:00 PM The ﬁrst exam will be Friday, September 25 in class. It will cover primarily Chapter 2 in the Griﬃths text. Chapter 1 contains necessary mathematical background. 1. Imagine a spherical shell of radius a and charge Q . Suppose a small circular patch with radius b is removed from the shell. (Assume that b ± a .) Show that the magnitude of electric ﬁeld inside of this hole at a radius a is Q/ (8 π±0 a 2 ). 2. Consider a spherical shell of radius R and charge Q . Show that the net force exerted on the top half of the shell by the bottom half of the shell is Q 2 / (32 π±0 R 2 ). Be careful what value you use for the electric ﬁeld in the computation! (Read Section 2.5.3.) 3. A sphere of radius R carries a charge density ρ ( r ) = kr 2 (where k is constant). Find the energy of this charge conﬁguration. There are two diﬀerent ways to get the solution (Eqs. 2.43 and 2.45) – do it both ways and show they produce the same result. 4. (a) Show that the electrostatic energy of a uniformly charged solid sphere, with total charge
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This note was uploaded on 01/20/2012 for the course PHYSICS 331 taught by Professor Staff during the Fall '09 term at Indiana.