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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 .

Respuesta :

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, ([tex]B_n = 4B[/tex]) and the time required for the rod to move is decreased by a factor of 2 ([tex]t_n = t/2[/tex]), the induced EMF becomes:

[tex]V_n = -(B_nA)/t_n[/tex]

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

The EMF has increased by a factor of 8.

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