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A very small circular loop of radius a i...

A very small circular loop of radius a is initially (at t = 0) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current I flows in the larger loop. The smaller loop is rotated with a constant angular speed `omega` about the common diameter. The emf induced in the smaller loop as a function of time t is

A

`(pi a^(2)mu_(0)I)/(2b)omega cos (omega t)`

B

`(pi a^(2)mu_(0)I)/(2b)omega sin (omega^(2)t^(2))`

C

`(pi a^(2)mu_(0)I)/(2b)omega sin (omega t)`

D

`(pi a^(2)mu_(0)I)/(2b)omega sin^(2)(omega t)`

Text Solution

Verified by Experts

The correct Answer is:
C
The situation is shown in the figure.
The magnetic field at the common centre due to the current in larger loop is
`B_(l)=(mu_(0))/(4pi)(2pi I)/(b)=(mu_(0)I)/(2b)`
where subscript l refers to larger loop.
The magnetic flux linked with the smaller loop at time t is
`phi_(s)=B_(l)A_(s)cos omega t`
where subscript s refers to smaller loop.
`phi_(s)=(mu_(0)I)/(2b)pi a^(2)cos omega t`
The emf induced in the smaller loop is
`epsilon_(s)=-(d phi)/(dt)=-(d)/(dt)((mu_(0)I pi a^(2))/(2b)cos omega t)=(mu_(0)I pi a^(2))/(2b) omega sin omega t`
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