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A circular loop of wire of radius R lies in the xy-plane, where a time-varying, radially...

A circular loop of wire of radius R lies in the xy-plane, where a time-varying, radially symmetric magnetic field of magnitude B = k r t3  (in SI units) points in the positive z-direction. Here, t is time, r is the distance from the centre of the loop, and k is a positive constant.

(i)   What must be the SI units of k ?   

(ii) Calculate the magnetic flux Φm through the loop as a function of time t.   

(iii) Calculate the magnitude of the emf ε induced in the loop as a function of time, and state the direction (viewed from the positive z-axis) in which current will flow.  

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