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A toroidal solonoid with N windings and current I has its central axis oriented along the z-axis. The cross section of the toroid surface upon which the windings are wound is rectangular with height h along the z-axis from z= -h/2 to z= +h/2. The inner and outer radii of the toroid are R1 and R2, respectively.
Find the magnetic field within the z=0 plane as a function of the radial distance s from the central axis.
Find the magnetic vector potential within the z=0 plane as a function of the radial dstance s fom the central axis.
Sketch what the vector potential looks like in this plane.
Describe how the toroidal solonoid or toroidal magnetic field can be used to observe the Aharonov-Bohm effect.
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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