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Question

Two conducting circular loops of radii R1 and R2 are placed in the same plane, with their centers coinciding. If R1>>R2, the mutual inductance M between them will be directly proportional to -

A
R22R1
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B
R1R2
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C
R2R1
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D
R21R2
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Solution

The correct option is A R22R1
Two concentric coils are of radius R1 and R2 as shown in the figure.


Let current in bigger loop be i.

Magnetic field at the center,

B=μ0i2R1

Magnetic flux through smaller coil,

ϕ=BA=μ0i2R1×πR22

ϕ=μ0πiR222R1

As per definition, ϕ=Mi

M=ϕi=μ0πiR222R1i

M=μ0πR222R1

MR22R1

Hence, option (A) is the correct answer.

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