Question

A conducting rod moves perpendicularly through a uniform magnetic field. How does the emf change if the magnetic field is increased by a factor of 4 and the time required for the rod to move through the field is decreased to half of the original time?

a) It increases by a factor of 2
b) It increases by a factor of 4
c) It increases by a factor of 8
d) It increases by a factor of 16 .

Answer 1

c) It increases by a factor of 8

Step-by-step explanation:

According to Faraday's law (and Lenz' law), the induced EMF is given as the rate of change of magnetic flux.

Mathematically:

V = -dФ/dt

Magnetic flux, Ф, is given as:

Ф = BA

where B = magnetic field strength and A = Area of object

Hence, induced EMF becomes:

V = -d(BA)/dt or -BA/t

If the magnetic field is increased by a factor of 4, (
`B_n = 4B`) and the time required for the rod to move is decreased by a factor of 2 (
`t_n = t/2`), the induced EMF becomes:

`V_n = -(B_nA)/t_n`

`V_n = (-4BA)/((t/2))\\\\V_n = (-8BA)/(t) \\\\V_n = 8V\\`

The EMF has increased by a factor of 8.