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

Options

A.
B.
C.
D.

Answer

C

Explanation

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).