A coil of effective area 3 ~m ^2 is placed at right angles to a magnetic field of induction 0.05 ~Wb / m ^2 . If the field is decreased to 20 % of its original value in 10 second, the e.m.f. induced in the coil will be

Step-by-step solution

Faraday’s Law gives the induced e.m.f. as ε = - d _B dt , where magnetic flux is _B = B A . The coil is perpendicular to the field so = 0^ and = 1 . Area A = 3~ m ^2 remains constant. The magnetic field decreases from B₁ = 0.05~ Wb / m ^2 to B₂ = 0.01~ Wb / m ^2 over t = 10~ s , giving B = -0.04~ Wb / m ^2 . The change in flux is _B = A B = 3 (-0.04) = -0.12~ Wb . The induced e.m.f. is = - _B t = - -0.12 10 = 0.012~ V . Converting to millivolts: 0.012~ V = 12~ mV . Final answer: 12~ mV