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ECE309-2008-hw6

# ECE309-2008-hw6 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 6 — Laplace’s Equation, the Method of Images, Current, and Magnetic Fields Due: Wednesday, October 22 1. Find the average potential over a spherical surface of radius R due to a point charge q located outside the sphere and show that this is equal to the potential at the center of the sphere. 2. Two infinite insulated conducting planes maintained at potentials 0 and V 0 form a wedge- shaped configuration, as shown below. Determine the potential distributions for the regions: (a) 0 < φ < α and (b) α < φ < 2 π . 3. In class, we found the potential and surface charge of a grounded conducting sphere when a point charge, q was placed a distance s from the center of the sphere. Use the method of images to find the potential for r > R and surface charge for the case where the sphere (of radius R ) is held at a potential V 0 6 = 0 (relative, of course, to a reference potential of zero at infinity). Find the force of attraction between the point charge, q , and the neutral conducting sphere.

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ECE309-2008-hw6 - ECE 309 Electromagnetic Fields University...

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