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Physics: mutual inductance

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A.) Show that the mutual inductance between two coaxial coils separated by a distance z as in figure attatched, one of radius a and N_a turns, and the other of radius b << a and N_b turns is:

pi*mu_0*N_a*N_b*a^2*b^2/[2(a^2 + z^2)^(3/2)]

Calculate the magnetic flux through coil b due to the current through coil a.

B.) How does the mutual inductance vary when the small coil is rotated around the vertical axis?

C.) What if one rotated the large coil around a vertical axis? Would the mutual indictance vary in the same way?

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Mutual inductance between two coaxial coils separated by a distance is determined.

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A.) Show that the mutual inductance between two coaxial coils separated by a distance z as in the figure, one of radius a and Na turns and the other of radius b << a and Nb turns is:

Пμ0NaNba2b2/[2(a2 + z2)(3/2)]

You should calculate the magnetic flux through coil b due to the current through coil a.

B.) How does the mutual inductance vary when the small coil is rotated around the vertical axis?

C.) What if one rotated the large coil around a vertical axis? Would the mutual inductance vary in the same way?

Solution:

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