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  • A rectangular loop of sides ‘ a ‘ and ‘ b ‘ is placed in xy plane. A very long wire is also placed in xy plane such that side of length ‘ a&nb

A rectangular loop of sides ‘ a ‘ and ‘ b ‘ is placed in xy plane. A very long wire is also placed in xy plane such that side of length ‘ a ‘ of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is ‘ d ‘. The mutual inductance of this system is proportional to :

Option: 1

a


Option: 2

b


Option: 3

1/d


Option: 4

Current in wire


Answers (1)

best_answer

The flux in a rectangular loop due to current i in wire is

\phi = \int_{d}^{d+b}\frac{\mu _{0}i}{2\pi x}\, \,adx= \frac{\mu _{0}ia}{2\pi }\iota n\frac{b+d}{d}

Mutual inductance is  

M=\frac{\phi }{i}=\frac{\mu _{0}a}{2\pi }\ln\frac{b+d}{d}

\therefore Mutual inductance is proportional to ‘a’.

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manish

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