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A long solenoid 'S' has 'n' turns per me...

A long solenoid 'S' has 'n' turns per meter, with diameter 'a'. At the centre of this coil, we place a smallar coil of 'N' tunrs and diameter 'b' (where b lt a). If the current in the solenoid increase linearly with time, what is the induced emf apperaing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of `mt^(2) + C`.

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C
As per the data given in the question, magnetic field due to current in soleniod `S,B=mu_(0)nl`
Magnetic flux linked with the smaller coil due to this field is
`phi=NBA`, where A = area of smaller coil `:.` emf induced in the smaller coil,
`epsi=-(dphi)/(dt)=-(d)/(dt)(NBpib^(2))`
`=-Npib^(2)(dt)/(dt)(mu_(0)n)=-Npib^(2)mu_(0)(dl)/(dt)`
As current I varies as a function of `(mt^(2)+C)`
`:.epsi=-Nnpimu_(0)b^(2)(d)/(dt)(mt^(2)+C)`
`=-Nnpimu_(0)b^(2)(2mt)" "....(i)`
From (i), `|epsi|propt`
So correct option is (c).
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