A square conducting loop of side 0.40m, mass 0.18kg, and resistance 0.60Ω is held horizontally and released from rest so that it falls vertically into a region where a uniform downward magnetic field B exists only within a horizontal slab of thickness 0.50m. The field is perpendicular to the plane of the loop. Neglect air resistance.
(a) Using symbols only, obtain an expression for the induced current in the loop when its lower edge has just entered the magnetic field region with downward speed v.
(b) Derive an expression for the magnetic force acting on the loop at this instant.
(c) Hence show that as the loop continues to fall inside the field, it approaches a constant terminal speed vt and obtain vt in terms of B, the side length a, mass m, resistance R, and acceleration due to gravity g.
(d) Prove that the rate at which mechanical potential energy is lost by the loop at terminal speed equals the rate of Joule heating in the loop.
(e) Evaluate the numerical value of vt for B=0.65T.