A coil of wire containing N turns is in an external magnetic field that is perpendicular to the plane of the coil and it steadily changing.Under these circumstances,an emf ε is induced in the coil.If the rate of change of the magnetic field and the number of turns in the coil are now doubled (but nothing else changes),what will be the induced emf in the coil?
A)2ε
B)ε/2
C)4ε
D)ε/4
E)ε

Question

Quizplus · Accepted Answer

According to Faraday's law of electromagnetic induction, the induced emf ε in a coil is given by the equation:

ε = -N(dΦ/dt)

where N is the number of turns in the coil and dΦ/dt is the rate of change of the magnetic flux through the coil.

When the rate of change of the magnetic field is doubled, the magnitude of dΦ/dt will also be doubled. If the number of turns in the coil is also doubled, the total magnetic flux through the coil will be doubled as well. Substituting these values in the above equation, we get:

ε' = -2N(2dΦ/dt)

ε' = -4N(dΦ/dt) = 4ε

Therefore, the induced emf in the coil is 4 times the original value, and the correct answer is C) 4ε.

A Coil of Wire Containing N Turns Is in an External