Mutual inductance in the figure shown is -

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Question: Answered & Verified by Expert

Mutual inductance in the figure shown is -

PhysicsElectromagnetic InductionJEE Main

Options:

A Zero
B $\frac{μ_{0} b}{2 π} \log_{e} \frac{a}{b}$
C $\frac{μ_{0} b}{2 π y} \log_{e} (1 + \frac{b}{a})$
D $\frac{μ_{0} b}{2 π} \log_{e} (1 + \frac{a}{b})$

Solution:

2407 Upvotes Verified Answer

The correct answer is:

\frac{μ_{0} b}{2 π} \log_{e} (1 + \frac{a}{b})

ϕ = M I = \int B . d A

M I = \int_{a}^{a + b} \frac{μ_{0} I}{2 π x} \times b d x

M = \frac{μ_{0} b}{2 π} \int_{a}^{a + b} \frac{d x}{x}

M = \frac{μ_{0} b}{2 π} \log_{e} [\frac{a + b}{a}]

M = \frac{μ_{0} b}{2 π} \log_{e} [1 + \frac{b}{a}]

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