A magnetic field induction is changing in magnitude at a constant rate dB dt . The plane of a circular loop of radius r of copper wire (mass m and radius a ) is placed perpendicular to the field. The induced current in the loop is = specific resistance, = density of copper

Step-by-step solution

The induced electromotive force in the circular loop is given by Faraday's law of induction: E = A dB dt = r^2 dB dt The resistance of the copper wire forming the loop is: R = l A' = 2 r a^2 The induced current in the loop is: I = E R = r^2 dB dt 2 r a^2 = r a^2 2 dB dt The mass of the copper wire is the product of its volume and density: m = ( a^2)(2 r) = 2 ^2 a^2 r Rearranging the above expression yields: r a^2 = m 2 Substituting this into the expression for the induced current, we get: I = 1 2 ( m 2 ) dB dt = m