A circular coil of radius 7 cm and 40 turns is rotated about its vertical diameter with an angular speed of 40 radians per second in a uniform horizontal magnetic field of 4 10⁻² T . What is the maximum current induced in the coil if the resistance of the coil is 11 ?

Step-by-step solution

Given: Number of turns, N = 40 Radius of the coil, r = 7 cm = 0.07 m Angular speed, = 40 rad/s Magnetic field, B = 4 10⁻² T Resistance, R = 11 The maximum induced emf in the coil is given by: _ max = N B A Substituting the area A = r^2 : _ max = 40 (4 10⁻²) ( 22 7 (0.07)^2 ) 40 _ max = 1600 4 10⁻² 22 7 49 10⁻⁴ _ max = 64 22 7 10⁻⁴ = 0.9856 V The maximum induced current is: I_ max = _ max R I_ max = 0.9856 11 = 0.0896 A I_ max = 89.6 mA 90 mA Answer: 90 mA