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Consider two conducting parallel in finite flat plates of equal charge density but opposite sign (e.g. a charged capacitor). Let the plates be separated by a distance d. Let the left plate be at the origin (x = 0) in the z-y plane and be defined to be the zero potential. Find the potential of the right plate. Find the potential as a function of x within the three regions of space that involve this configuration of charge.
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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