Mutual Inductance - 7-27-2020

One closed loop of thin wire has the following shape:

x 1 = cos θ 1 y 1 = sin θ 1 z 1 = 0 x_1 = \cos \theta_1 \\ y_1 = \sin \theta_1 \\ z_1 = 0

Another closed loop of thin wire has the following shape:

x 2 = cos θ 2 y 2 = sin θ 2 z 2 = 1 x_2 = \cos \theta_2 \\ y_2 = \sin \theta_2 \\ z_2 = 1

What is the mutual inductance between the two loops?

Note: Magnetic permeability μ 0 = 1 \mu_0 = 1
Bonus: If this problem seems familiar or repetitive, try solving it a different way than usual


The answer is 0.393.

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1 solution

Talulah Riley
Jul 27, 2020

Nice problem.
I have used little bit symmetry.

Feel free to ask me anything in my solution.

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