A semicircular loop of radius r is positioned on the axis of a large current-carrying circular ring of radius R (with R r). The loop is placed at an axial distance of R*sqrt(3) from the center of the ring, and the plane of the semicircular loop makes an angle of 53 deg with the plane of

Question

A semicircular loop of radius r is positioned on the axis of a large current-carrying circular ring of radius R (with R >> r). The loop is placed at an axial distance of R*sqrt(3) from the center of the ring, and the plane of the semicircular loop makes an angle of 53 deg with the plane of the ring. Find the mutual inductance M between the two coils.

Accepted Answer

mu0*pi*r² / (40*R). The axial field at distance R*sqrt(3) simplifies to mu0*I/(16R). The effective area of the semicircular loop projected onto the field direction is (pi*r²/2)*cos(37 deg) = (pi*r²/2)*(4/5). Dividing flux by I gives M = mu0*pi*r²/(40R).

Solution

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