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The gap between two concentric conducting spheres of radii a and b (with b > a) is filled with a material of resistivity rho. Find the electrical resistance measured between the inner and outer spheres.

1. rho/(4*pi) * (1/a - 1/b)
2. rho/(2*pi) * (1/a - 1/b)
3. rho/(2*pi) * (1/a + 1/b)
4. rho/(4*pi) * (1/a + 1/b)

Correct answer: rho/(4*pi) * (1/a - 1/b)

Solution

Summing radial shell resistances gives R = (rho/4pi)(1/a - 1/b), since the cross-sectional area at radius r is 4*pi*r².

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