Two circular coils one of smaller radius r1 and other of very large radius r2 are placed coaxially with centers coinciding.obtain the mutual inductance of the arrangement.
Answers
The mutual inductance of the arrangement is M = μo πR^2 / 2R
Explanation:
Suppose a current I2 flows through the outer coil.
Magnetic field at the centre of the coil is.
B2 = μoI2 / 2R
Magnetic field B2 may be considered constant over the cross sectional area of the smaller inner coil.
Hence
ϕ = B.A
ϕ1 = πR^2B2
ϕ1 = μo πR^2 I2 / 2R
ϕ1 = MI2
M = ϕ1 / I2 = μo πR^2 / 2R
Thus the mutual inductance of the arrangement is M = μo πR^2 / 2R
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