A coil having area \( A_o \) is placed in a magnetic field. The magnetic field is perpendicular to the plane of the coil. When the magnetic field changes from \( B_o \) to \( 4B_o \) in a time interval t, the magnitude of emf induced in the coil will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \frac{3A_oB_o}{t} \)
By Faraday's law the magnitude of the induced emf is the rate of change of magnetic flux. The field is perpendicular to the coil, so \( \Phi = B A_o \), and the area stays fixed.
\( \displaystyle \varepsilon = \frac{\Delta\Phi}{t} = \frac{A_o\,(4B_o - B_o)}{t} = \frac{3A_oB_o}{t} \)