A long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the center 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 nature of variation in emf, if current varies as a function of mt 2 + C.

A long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the center 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 nature of variation in emf, if current varies as a function of mt² + C.

magnetic field due to a solenoid S,

magnetic flux in smaller coil

where A = πb²

so

where negative sign indicates opposite nature of induced EMF the magnitude of EMF varies with time as shown as fig

1