hw3 - Electricity and Magnetism I(P331 Homework 3 Due...

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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.
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