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Consider a thin ring of radius a with uniform charge density and total charge Q. The ring is cut in half across the diameter and the two halves superimposed to double the effective charge density. Calculate the electric field at a point 4a from the ring along the x-axis with the ring in the y-z plane and the center of the arc at the origin. The half-ring is symmetric about the z-x plane extending only in the positive z-direction.
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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