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A variable capacitor consists of two thin coaxial metal cylinders of radii a and b, with (b-a)<<a, free to move with respect to each other in the axial direction. The length of the cylinders is L, and the potential difference between the two cylinders is V. Using energy methods, find the magnitude and direction of the force on the inner cylinder when it is displaced by a small amount with respect to the outer one. Expain how this force arises.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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