Problem 19P

A toroidal coil has a rectangular cross section, with inner radius a, outer radius a + w, and height h. It carries a total of N tightly wound turns, and the current is increasing at a constant rate (d I/dt = k). If w and h are both much less than a, find the electric field at a point z above the center of the toroid. [Hint: Exploit the analogy between Faraday fields and magnetostatic fields, and refer to Ex. 5.6.]

Solution 19P

Step 1 of 3:

Consider a toroidal coil has rectangular cross section having an inner radius and outer radius , at a height . The toroid carries tightly wound turns.

The magnetic field outside the toroid is zero.

The magnetic field inside the toroid is,

Where is the current flowing through the toroid.

is the number of turns.