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A 65-turn circular coil (radius = 31 cm) with a total resistance of 5.4 ? is...

A 65-turn circular coil (radius = 31 cm) with a total resistance of 5.4 ? is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of this field varies with time according to B = A sin(?t), where the amplitude is A = 110 ?T and the angular frequency is ? = 50 ? rad/s. What is the magnitude of the current (in mA) induced in the coil at t = 39 ms?

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Answer #1

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Answer #2

Magnetic field at t=39 ms

B=(110)Sin(50pi*39*10-3)

B=-17.2 uT

Area of circular coil

A=pi*r2=pi*0.312=0.302 m2

Induced emf

E=NBAW =65*(17.2*10-6)*0.302*50pi

E=0.053 Volts

Induced current

I=E/R=0.053/5.4

I=9.82*10-3 A or 9.82 mA

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