In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options.

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The mutual inductance between the two is $\frac{μ_{o} a}{2 π} \ln (2)$

The mutual inductance between the two is $\frac{μ_{o} a^{2}}{2 π} \ln (2)$

If a constant current is passed in the straight wire in upward direction and loop is brought close to the wire, then induced current in the loop is clockwise

In the above condition, induced current in the loop is anti-clockwise.

answer is A, C.

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Detailed Solution

$B_{x} = \frac{μ_{o}}{2 π} \frac{i}{x} d ϕ = (B_{x}) d S = (\frac{μ_{o}}{2 π} \frac{i}{x}) (a d x) ϕ = \int_{a}^{2 a} d ϕ = \frac{μ_{o} i a}{2 π} \ln 2 M = \frac{ϕ}{i} = \frac{μ_{o} a}{2 π} \ln 2$

(c)

Wire produces $⊙$ magnetic field over the loop. If the loop is brought closer to the wire $⊙$ magnetic field passing through the loop increases. Hence, induced current produces $\otimes$ magnetic field so, induced current is clockwise.

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