Question

(a) Write down Faraday's Law of electromagnetic induction. Define all of the terms used and state any sign conventions employed. 

(b) A circular loop of wire, radius \(a\), and resistance \(R\), is threaded by a time-varying, externally applied magnetic field that is always normal to the plane of the wire. The magnetic field has a magnitude \(B=B_{0}(1+\alpha t)\).

(i) Derive an expression for the induced emf, current and electric field around the loop and hence the current flowing in the wire. Show in a diagram the direction of the induced current when the magnetic field points upwards through the loop. In these calculations you may ignore the magnetic field generated by the induced current. 

(ii) How would the emf, current and electric field around the loop change if the wire is replaced by a loop of insulating material?

(c) The experiment in part (b) is repeated using a superconducting loop wire, i.e., it now has zero resistance. What is the rate of change of total flux through the loop of wire now?

(d) A magnet with its N-S axis aligned vertically falls through a conducting copper pipe. Without detailed calculation, draw the directions of the induced currents in the pipe (eddy currents), the magnetic field induced by these currents and the resulting Lorentz force acting on the magnet. Explain why the rate of descent of the magnet depends on the resistance and thickness of the pipe.

Answer 1