Question

The formula for induced e.m.f. in a coil due to change in magnetic flux through the coil is (here A = area of the coil, B = magnetic field)
(a) $e=-A.\frac{dB}{dt}$
(b) $e=-B.\frac{dA}{dt}$
(c) $e=-\frac{d}{dt}(A.B)$
(d) $e=-\frac{d}{dt}(A\times B)$

Answer 1

answer : option (c) $e=-\frac{d}{dt}(A.B)$

explanation : induced electromotive force (e.g., emf ) in a coil to change in magnetic flux through the coil is negative of rate of change of magnetic flux with respect to current.

e.g., $e=-\frac{d\phi}{dt}$

but we know, magnetic flux is the dot product of magnetic field and cross sectional area of the coil.

so, $\phi=\vec{B}.\vec{A}$ or $\vec{A}.\vec{B}$

hence, induced emf , e = - $\frac{d(A.B)}{dt}$

so, option (c) is correct.