A long solenoid S has n turns per meter, with a diameter a. At the centre of this coil, we place a smaller coil of N turns and diameter b (where b<a). If the current in the solenoid increases linearly, with time, what is the induced emf appearing in the smaller coil. Plot graph showing the nature of variation in emf, if current varies as a function of mt2+C.

Hint: The current is induced due to the change in magnetic flux.
Step 1: Magnetic field due to a solenoid S, B=μ0ni where signs are usual.
Magnetic flux in smaller coil, ϕ=NBA, where A=πb2
Step 2: Applying Faraday's law of EMl, we have;
e=-dϕdt=-ddtNBA
=-Nπb2dBdt
where, B=μ0Ni
=-Nnπμ0b2ddtmt2+C=-μ0Nnπb22mt
Since the current varies as a function of mt2+C.
e=-μ0Nnπb22mt