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F07_hw04

# F07_hw04 - Physics 505 Fall 2007 Homework Assignment#4 —...

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Unformatted text preview: Physics 505 Fall 2007 Homework Assignment #4 — Due Thursday, October 4 Textbook problems: Ch. 3: 3.1, 3.2, 3.4, 3.7 3.1 Two concentric spheres have radii a , b ( b > a ) and each is divided into two hemispheres by the same horizontal plane. The upper hemisphere of the inner sphere and the lower hemisphere of the outer sphere are maintained at potential V . The other hemispheres are at zero potential. Determine the potential in the region a ≤ r ≤ b as a series in Legendre polynomials. Include terms at least up to l = 4. Check your solution against known results in the limiting cases b → ∞ , and a → 0. 3.2 A spherical surface of radius R has charge uniformly distributed over its surface with a density Q/ 4 πR 2 , except for a spherical cap at the north pole, defined by the cone θ = α . a ) Show that the potential inside the spherical surface can be expressed as Φ = Q 8 π ∞ X l =0 1 2 l + 1 [ P l +1 (cos α )- P l- 1 (cos α )] r l R l +1 P l (cos θ ) where, for l = 0,...
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F07_hw04 - Physics 505 Fall 2007 Homework Assignment#4 —...

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