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`.

Explanation

Magnetic field due to a solenoid `S, B =mu_0nl` where signs are as usual .
Magnetic flux in smaller coil `phi=NBA` where `A=pib^2`
Applying Faraday's law of EMI, we have
So, `e=(dphi)/(dt)=(-d)/(dt)(NBA)`
`=-Npib^2(d(B))/(dt)`
where, `B=mu_0Ni`
`=-Npib^2mu_0n(dl)/(dt)`
`=-Nnpimu_0b^2(d)/(dt)(mt^2+c)=-mu_0Nnpib^(2)2mt`
Since, current varies as a function of `mt^2+C`.
`e=-mu_0Nnpib^(2)2mt`