A magnetic field 4 10⁻² ~T acts at right angles to a coil of area 100 ~cm ^2 with 50 turns. The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time ' t '. The value of ' t ' is

Step-by-step solution

Faraday's law gives the average induced emf as = N | _B t | . The magnetic flux through a coil perpendicular to a uniform magnetic field is _B = B A . The area is A = 100 cm ^2 = 10⁻² m ^2 . The initial flux is _i = (4 10⁻²) (10⁻²) = 4 10⁻⁴ Wb and final flux is zero, so _B = -4 10⁻⁴ Wb . Substituting N = 50 and = 0.1 V , we get 0.1 = 50 4 10⁻⁴ t . Solving for t : t = 50 4 10⁻⁴ 0.1 = 2 10⁻² 10⁻¹ = 2 10⁻¹ = 0.2 s . The correct answer is 0.2 second.