Problem:

Show that the magnitude of the magnetic field B at the center of a loop of wire carrying a current I and shaped like a regular plane polygon of 2n sides, the distance between parallel sides being 2a, is 
[nμ0I/(πa)]sin(π/2n),
using the Biot-Savart law.  The n = 3 case is shown.

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Solution:

Problem:

A large number, N, of closely spaced turns of fine wire are wound in a single layer upon the surface of a wooden sphere of radius R, with the planes of the turns perpendicular to the axis of the sphere and completely covering its surface.  If the current in the windings is I, determine the magnetic field at the center of the sphere.

Solution:

Problem:

What current is required in the windings of a long solenoid that has 1000 turns uniformly distributed over a length of 0.4 m in order to produce at the center of the solenoid a magnetic field of 10-4T?

Solution: