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# HW-4 - Homework#4 1 A metal sphere of radius R carrying...

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Homework #4 1. A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge. (a) Find the surface charge density at R, at a, and at b. (b) Find the potential at the center, using infinity as the reference point. (c) Now the outer surface is touched to a ground wire, which lowers its potential to zero (same as at infinity). How do your answers to (a) and (b) change? 2. A metal sphere of radius R carries a total charge Q. What’s the force of repulsion between the “northern” and “southern” hemisphere? 3. An inverted hemispherical bowl of radius R carries a uniform surface charge density . Find the potential difference between the “north pole” and the center. 4. A sphere of radius R carries a charge density =kr (where k is a constant). Find the energy of the configuration (taking infinity as the reference point). 5. Two infinitely long wires running parallel to the x axis (in xy plane) carry uniform charge density +

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HW-4 - Homework#4 1 A metal sphere of radius R carrying...

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