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

Answer:

c) It increases by a factor of 8

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:

$V_n = -(B_nA)/t_n$

$V_n = \frac{-4BA}{(t/2)}\\\\V_n = \frac{-8BA}{t} \\\\V_n = 8V$

The EMF has increased by a factor of 8.