A circular loop of wire with radius 0.0410m and resistance 0.158? is in a region

Question

A circular loop of wire with radius 0.0410m and resistance 0.158? is in a region of spatially uniform magnetic field, as shown in the following figure (Figure 1). The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.36Tand is decreasing at a rate of -0.642T/s .

What is the rate at which electrical energy is being dissipated by the resistance of the loop?

A circular loop of wire with radius 0.0410m and resistance 0.158? is in a region of spatially uniform magnetic field, as shown in the following figure (Figure 1). The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.36Tand is decreasing at a rate of -0.642T/s . What is the rate at which electrical energy is being dissipated by the resistance of the loop?

Explanation / Answer

Area

A=pi*r2=pi*0.0412=5.28*10-3 m2

Induced emf

E=A(dB/dt)=(5.28*10-3)*0.642

E=3.4*10-3 Volts

Energy dissipated in resistor is

P=E2/R =(3.4*10-3)2/0.158

P=7.38*10-5 W

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