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A small square loop of wire of side l is...

A small square loop of wire of side l is placed inside a large square loop of wire of side `L(gtgtl)`. The loops aer coplanar and their centres coincide. What is the mutual inductance of the system?

A

`l//L`

B

`l^(2)//L`

C

`L//l`

D

`L^(2)//l`

Text Solution

Verified by Experts

The correct Answer is:
B
Magnetic field produced by a current `I` in a larger square loop at its centre,
`B prop (I)/(L) rArr B = K(I)/(L)`
`:.` Magnetic flux linked with the smaller loop,
`phi = BS rArr phi = (K (I)/(L)) (l^(2))`
Therefore, the mutual inductance `M = (phi)/(I) = K(l^(2))/(L)` or `M prop (l^(2))/(L)`
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Knowledge Check

  • A small square loop of wire of side l is placed inside a large square loop of wire of side L (L gt gt l) . The loops are coplanar and their centre coincide. What is the mutual inductance of the system ?

    A
    `2sqrt2(mu_(0))/(pi)(l^(2))/(L)`
    B
    `8sqrt2(mu_(0))/(pi)(l^(2))/(L)`
    C
    `2sqrt2(mu_(0))/(2pi)(l^(2))/(L)`
    D
    `2sqrt2(mu_(0)L^(2))/(pil)`