A square-shaped copper coil with edges of length 50 cm contains 50 turns. It is placed perpendicular to a 1.0 T magnetic field. The coil is removed from the magnetic field in 0.25 s and restored to its original place in the subsequent 0.25 s . The resistance of the coil is 25 . Assuming the coil moves with uniform velocity during its removal and restoration, determine the thermal energy developed in the coil during i

Step-by-step solution

Area of the coil, A = 0.5 0.5 = 0.25 m ^2 . Initial magnetic flux through the coil, _i = NBA = 50 1.0 0.25 = 12.5 Wb . Since the coil moves with uniform velocity, the rate of change of flux is constant. During removal, the induced emf is: E₁ = t = 12.5 0.25 = 50 V Thermal energy developed during removal is: H₁ = E₁^2 R t = (50)^2 25 0.25 = 100 0.25 = 25 J Similarly, during restoration, the magnitude of the induced emf remains the same because the change in flux and time taken are identical: E₂ = 50 V Thermal energy