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A cylindrical capacitor of a length L consists of a conductive wire of radius a at the centre, surrounded by a concentric thin conductive shell of radius b. The space between the conductive wire and the thin shell is filled with a dielectric material of permitivity.
(a) If the charge carried by the capacitor is Q, neglecting the edge effects (fringing field), find the electric field as a function of radial distance r.
(b) Find the capacitance of this capacitor.
(c) Suppose this capacitor is connected to a battery of potential U, when the dielectric material is partially pulled out of the capacitor with a length of Z outside the capacitor, neglecting the edge effects, find the magnitude and direction of the force that needs to apply in order to move the dielectric material to this position.
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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