A square loop of side length 0.5 ~m is made of a uniform wire. It is slowly and uniformly pulled completely out of a uniform magnetic field of magnitude 0.4 ~T in 1 ~s . The magnetic field is perpendicular to the plane of the loop. Assume all the mechanical work done by the external agent is dissipated as heat in the wire. If the resistivity of the wire material is 2 10⁻⁸ m , its density is 5000 ~kg/m ^3 , and its sp

Step-by-step solution

Let the side length of the square loop be l , and the cross-sectional area of the wire be A_c . The total length of the wire is 4l . The resistance of the loop is R = 4l A_c . The mass of the loop is m = d (4l) A_c . When the loop is pulled out with a constant velocity v = l t , the motional EMF induced is = B l v . The induced current is i = R = B l v R . The magnetic force opposing the motion is F = i l B = B^2 l^2 v R . The work done by the external agent to pull it completely out (distance l ) is: W = F l = B^2