A small circular coil of turns and resistance is coaxially placed at the centre of a…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A small circular coil of N turns and resistance r is coaxially placed at the centre of a long solenoid of n turns per unit length and cross-sectional area A. The current in the solenoid is increased uniformly from zero to I0 in a time interval Δt.
Answer all parts carefully.
(i) Derive an expression for the magnitude of the emf induced in the small coil in terms of μ0, n, A, N and the rate of change of current in the solenoid.
(ii) Using appropriate reasoning, decide the direction of the induced current in the small coil for the rising current in the solenoid.
(iii) Calculate the total energy dissipated as heat in the small coil during the interval Δt and show that it is equal to 21LI02, where L is the mutual inductance of the system.