A long solenoid S has n turns per metre, with radius a. At the centre of this coil, we place a smaller coil of N turns and radius b (where ). If the current in the solenoid increases linearly with time, what is the induced emf appearing in the smaller coil. Plot a graph showing nature of variation in emf, if current varies as a function of
Magnetic field caused by a solenoid is given by
.
Magnetic flux in the smaller coil is
where,
Applying Faraday's law of EMI, we have
So,
Where,
Since, current varies as a function of time, so
By solving
The negative sign signifies opposite nature of induced emf.