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 increases 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`.

Explanation

Magnetic field produced by long solenoid,
`B=mu_0 nI`
Magnetic flux linked with smaller solenoid,
`phi=NAB`
`=N(pib^2)(mu_0nI)`
`phi=mu_0Npib^2nI`
Induced emf in smaller solenoid ,
`epsilon=-(dphi)/(dt)=-d/(dt)(mu_0N n pi b^2I)`
`=-mu_0N n pib^2 (dI)/(dt)`
`=-mu_0Nnpib^2 d/(dt)(mt^2+C)`
`=-mu_0N n pib^2 m(2t)`
`=-(2mu_0 N n pib^2m)t`
`|epsilon|=(2mu_0Nnpib^2m)t` which is likely y=mx graph of induced emf `|epsilon|to t` is