A superconducting solenoid is to be designed to have an interior field of 7.171 T with a maximum current of 1000 A. The permeability of free space is 1.25664 * 10-6 T · m/A. How many windings are required on a 1 - meter solenoid length?

5706.5

Explanation:

B = 7.171 T, i = 1000 A, μ0 = 1.25664 x 10^-6 T m/A, l = 1 m

Let the number of turns be N.

The magnetic field due to a current carrying solenoid is given by

B = μ0 x N x i / l

B x l / (μ0 x i) = N

N = 7.171 x 1 / (1.25664 x 10^-6 x 1000)

N = 5706.5