A uniform magnetic field is changing in magnitude at a constant rate . We are given a mass of copper which is to be drawn into a wire of radius and formed into a circular loop of radius R. We have to show that the induced current in the loop does not depend on the size of the wire or of the loop and, assuming is perpendicular to the loop is given by

where is the resistivity and the density of the copper.

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As the radius of the copper wire is and its length is the mass of the wire

where is the density of copper and is the mass of the copper from which the wire has been drawn.

Resistance of this copper wire will be

where is the resistivity of the copper.

Magnitude of the induced emf in the loop due to changing magnetic field, , perpendicular to the plane of the loop is given by the Faraday’s law,

But

We recall that

which is independent of the size of the wire or that of the loop.