A circular loop of radius 27 cm is located in the plane of the paper inside a ho

Question

A circular loop of radius 27 cm is located in the plane of the paper inside a homogeneous magnetic field of 0.9 T pointing into the paper. It is connected in series with a resistor of 203 ?. The magnetic field is now increased at a constant rate by a factor of 2.1 in 29 s.

a) Calculate the magnitude of the induced emf in the loop during that time.

b) Calculate the current induced in the loop during that time.

c) Calculate the average induced voltage when the magnetic field is constant at 1.89 T while the loop is pulled horizontally out of the magnetic field region in 8.7 s.

Thanks!

Explanation / Answer

Here ,

A)

magnitude of emf induced , emf = change in magnetic flux/time

magnitude of emf induced , emf = pi*0.27^2 * 0.9(2.1 - 1)/29

magnitude of emf induced , emf = 0.0078 V

the magnitude of emf induced is 0.0078 V

B)

using Ohm's law

magnitude of induced current = induced emf /R

magnitude of induced current = 0.0078/203

magnitude of induced current = 3.84 *10^-5 A

the magnitude of induced current is 3.84 *10^-5 A

C)

magnitude of emf induced , emf = change in magnetic flux/time

magnitude of emf induced , emf = B*(A2 - A1)/time

magnitude of emf induced , emf = 1.89 * pi(0.27^2 - 0)/8.7

magnitude of emf induced , emf = 0.0497 V

the magnitude of emf induced is 0.0497 V

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