Electricity and Magnetism I (P331)Homework 3Due: Wednesday, September 23, 4:00 PMThe first exam will beFriday, September 25in class. It will cover primarily Chapter 2 in the Griffithstext. Chapter 1 contains necessary mathematical background.1. Imagine a sphericalshellof radiusaand chargeQ. Suppose a small circular patch with radiusbisremoved from the shell. (Assume thatba.) Show that the magnitude of electric field inside of thishole at a radiusaisQ/(8π0a2).2. Consider a sphericalshellof radiusRand chargeQ. Show that the net force exerted on the top halfof the shell by the bottom half of the shell isQ2/(32π0R2). Be careful what value you use for theelectric field in the computation! (Read Section 2.5.3.)3. A sphere of radiusRcarries a charge densityρ(r) =kr2(wherekis constant). Find the energy ofthis charge configuration. There are two different ways to get the solution (Eqs. 2.43 and 2.45) – doit both ways and show they produce the same result.
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