A square loop having 20 turns and a total resistance of 50 is placed in a uniform magnetic field of magnitude 0.5 ~T perpendicular to its plane. The loop is being pulled out of the magnetic field at various constant velocities v . A graph of the required external force F to maintain the constant velocity is plotted against v . The graph is a straight line passing through the origin with a slope of 0.08 ~N s/m . The s

Step-by-step solution

When a square loop of N turns and side length l is pulled out of a magnetic field B with velocity v , the motional EMF induced is: = N B l v The induced current in the loop is: i = R = N B l v R The magnetic force opposing the motion acts on the N turns of the leading/trailing edge of length l : F = N (i l B) = N ( N B l v R ) l B = N^2 B^2 l^2 R v Since the external force must balance this magnetic force to maintain constant velocity, the graph of F versus v is a straight line with slope m given by: m = N^2 B^2 l^