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A uniform thin ring of charge, with radius 3.80 centimeter and total charge 7.00 μC, is situated in the yz-plane and centered on the origin. (In other words, the x-axis passes through the center of the ring, and is perpendicular to the ring). A particle of mass 14.6 gram and charge 4.20 μC is on the negative x-axis, initially very far from the ring. The particle is launched in the positive x direction with some initial velocity, toward the center of the ring. Find the minimum initial velocity required for the particle to get past the center of the ring and come out the other side.
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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