A circular coil enclosing an area of 200 cm2 is made of 210 turns of copper wire

Question

A circular coil enclosing an area of 200 cm2 is made of 210 turns of copper wire. The wire making up the coil has resistance of 7.0 , and the ends of the wire are connected to form a closed circuit. Initially, a 1.4-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.4 T and points downward through the coil. If the time required for the field to reverse directions is 0.30 s, what is the average current in the coil during that time?

Explanation / Answer

B = 1.4 T   

area A = 200 cm2 = 200 x 10-4 m2

magnetic flux is  B = BACos where is the angle between the area vector A and magnetic field B

Initial magnetic flux is  BACos 0 = 1.4 x 200 x 10-4 x 1 = 0.028

Final magnetic flux = BA Cos 180 = 1.4 x 200 x 10-4 x - 1 = - 0.028

induced emf in coil is given by = - dB /dt

therefore = - dB /dt = - ( final magnetic flux - intial magnetic flux ) /dt

= - ( -0.028 - 0.028 ) / 0.30 = 0.056 / 0.3 = 0.186666666 Volts

this is for one loop or one turn, there are 210 such turns , so,

the net emf of all the loops /turns is 210 x 0.186666666 = 39.2 Volts

average Current = Votalge difference / Resistance = 39.2 / 7 = 5.6 A

Average current = 5.6 Amperes

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