A cirular wire wrapped 10 times with a radius of 0.01 meters and resistance of 1

Question

A cirular wire wrapped 10 times with a radius of 0.01 meters and resistance of 10 ohms is placed in the x-y plane. A uniform magnrtic field directed in the negative z direction changes in magnitud from 0.50 to 0.25 T in a time of 0.001 seconds.

a. What is the amount of the average induced EMF in the wire?

b. What is the amount and direction of the average induced current in the wire?

c. if the uniform magnetic field was 0.50 T in the negative z direction, What is the total magnetic field(amount and direction) at the center of the circular wire using the current found in part b?

Explanation / Answer

a)

Magnetic flux in the circular wire is

flux = N B A

emf induced in the wire is

emf = N A dB/ dt

= ( 10 ) pi ( 0.01 m ) ^2 (0.5 - 0.25 ) / 0.001 s

=0.785 V

b)

Induced current in the wire is

I = emf / R

= 0.785 / 10

= 0.0785 A

From thumb rule, the current direction is coutr clock wise. so the direction of induced current is a clock wise.

c)

Magnetic field at the center of circular wire is

B = mu_o I / 2 r

= ( 4 pi * 10 ^ - 7 ) ( 0.0785 A ) / 2 ( 0.01 m )

= 4.93*10^ -6 T

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