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The conducting circular loops of radii R...

The conducting circular loops of radii `R_(1) and R_(2)` are placed in the same plane with their centres coinciding. If `R_(1) gt gt R_(2)`, the mutual inductance M between them will be directly proportional to

A

`(R_(1))/(R_(2))`

B

`(R_(2))/(R_(1))`

C

`(R_(1)^(2))/(R_(2))`

D

`(R_(2)^(2))/(R_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let acurrent `I_(1)` flows through the outer circular col of radius `R_(1)`.
The magnetic field at the centre of the coil is
`B_(1)=(mu_(0)I_(1))/(2R_(1))`
As the inner coil of radius `R_(1)`placed co-axiallu has small radius `(R_(2)-R_(1))`, therefore, `B_(1)` may be takne constant over its corss-sectional area.
Hence, flux associated with the inne coil is
`phie_(2)B_(1)piR_(2)^(2)=(mu_(0)I_(1))/(2R_(1))piR_(2)^(2)`
As `M=(phi_(2))/(I_(1))=(mu_(0)R_(2)^(2))/(2R_(1))`
`:. M prop(R_(2)^(2)))/(R_(1))`
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