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A conducing circular loop is placed in a...

A conducing circular loop is placed in a uniform magnetic field of indution `B` tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate `(dr//dt)`. Then the induced e.m.f. at the instant when the radius is `r` is:

A

`pirB((dr)/(dt))`

B

`2pirB((dr)/(dt))`

C

`pir^(2)B((dr)/(dt))`

D

`pirBr^(2)/(2)((dr)/(dt))`

Text Solution

Verified by Experts

The correct Answer is:
B
If the radius is `r` at a time `t`, then the instantaneous magnetic flux `f` is given by:
`phi=pir^(2)B`
now, induced `e.m.f.e` is given by
`e=(dphi)/(dt)=-(d)/(dt)(pir^(2)B)=piB(2r(dr)/(dt))=2pirB(2r(dr)/(dt))`
induced e.m.f `2pirBr((dr)/(dt))` numerically`
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