1)A circular conducting loop of radius 29.0 cm is located in a region of homogen

Question

1)A circular conducting loop of radius 29.0 cm is located in a region of homogeneous magnetic field of magnitude 0.500 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 231 ?. The magnetic field is now increased at a constant rate by a factor of 2.40 in 31.0s.
Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

2)Calculate the magnitude of the current induced in the loop while the field is increasing.

3) With the magnetic field held constant at its new value of 1.20 T, calculate the magnitude of the average induced voltage in the loop while it is pulled horizontally out of the magnetic field region during a time interval of 2.10 s.

Explanation / Answer

The area of the loop is

A = pi * r^2 = 0.2642 m^2

Here,

Bi = 0.500 T
Bf = 2.40 Bi = 1.20 T
t = 31.0 s

As

emf = A(Bf - Bi)/t

emf = 5.966*10^-3 V or 5.966 mV   [ANSWER, PART A]

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As the loop is in series with the resistor,

I = emf / R

I = 2.58*10^-5 A or 0.0258 mA   [ANSWER, PART B]

******************

Now,

emf = B(Af - Ai)/t

As Ai = 0.2642 m^2, Af = 0 m^2, B = 1.20 T, t = 2.10 s,

emf = 0.151 V or 151 mV [ANSWER, PART C]

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