A flat coil of wire has an area A , N turns, and a resistance R . It is situated

Question

A flat coil of wire has an area A, N turns, and a resistance R. It is situated in a magnetic field, such that the normal to the coil is parallel to the magnetic field. The coil is then rotated through an angle of 90, so that the normal becomes perpendicular to the magnetic field. The coil has an area of 1.5 × 10-3 m2, 50 turns, and a resistance of 190 . During the time while it is rotating, a charge of 6.4 × 10-5 C flows in the coil. What is the magnitude of the magnetic field?

A flat circular coil with 159 turns, a radius of 4.84 x 10-2 m, and a resistance of 0.673 is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of B/t = 0.835 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.

Explanation / Answer

current through the coil, I = (6.4 x 10^-5) / t

induced emf = I R = 0.01216 / t

Induced emf = rate of change of magnetic flux

0.01216 / t = N A B w

0.01216 / t = (50) (1.5 x 10^-3) (B) ( pi / 2t )

0.0216 = 0.1178 B

B = 0.183 T ...........Ans

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induced emf = rate of change of magnetic flux

= N A dB/dt

= 159 x pi x (4.84 x 10^-2)^2 x 0.835

= 0.977 Volt

I = e / R = 1.45 A

magnetic field at the center, B = u0 I / 2 R

= (4 pi x 10^-7) (1.45) / (2 x 4.84 x 10^-2)

= 1.885 x 10^-5 T

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