Exercise 29.20 A circular loop of wire with radius 0.0460m and resistance 0.151

Question

Exercise 29.20 A circular loop of wire with radius 0.0460m and resistance 0.151 ohm is in a region of spatially uniform magnetic field, as shown in the following figure, . The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.21 T and is decreasing at a rate of -0.640 T/s. Part A Is the induced current in the loop clockwise or counterclockwise? Part B What is the rate at which electrical energy is being dissipated by the resistance of the loop?

Explanation / Answer

We know that

The induced emf is given by e =-dQB/dt =-A(dB/dt) =-pir2(dB/dt ) =-(3.14)(0.0460)2*(-0.640T/s) =4.25*10-3V

The induced current is I =e/R =4.25*10-3V/0.151ohm =0.028A

Now the power dissipated due to the resistance R is given by

P =I2*R =(0.028A)2(0.151ohm) =1.183*10-4W =0.118mW

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