Answer:
[tex]91.1\ \mu W[/tex]
Explanation:
P = Perimeter of loop = 34 cm
r = Radius
[tex]\frac{dB}{dt}[/tex] = Rate of change of magnetic field = 0.0633 T/s
A = Area = [tex]\pi r^2[/tex]
R = Resistance = 0.00372 Ω
Perimeter is given by
[tex]P=2\pi r\\\Rightarrow r=\frac{P}{2\pi}\\\Rightarrow r=\frac{0.34}{2\pi}\\\Rightarrow r=0.05411\ m[/tex]
Induced emf is given by
[tex]\epsilon=A\frac{dB}{dt}\\\Rightarrow \epsilon=\pi r^2\frac{dB}{dt}[/tex]
Induced current is given by
[tex]I=\frac{\epsilon}{R}\\\Rightarrow I=\left(\frac{1}{R}\pi r^2\frac{dB}{dt}\right)[/tex]
Power is given by
[tex]P=I^2R\\\Rightarrow P=\left(\frac{1}{R}\pi r^2\frac{dB}{dt}\right)^2 R\\\Rightarrow P=\frac{1}{R}\left(\pi r^2\frac{dB}{dt}\right)^2\\\Rightarrow P=\frac{1}{0.00372}\left(\pi 0.05411^2\times 0.0633\right)^2\\\Rightarrow P=9.11\times 10^{-5}\ W=91.1\ \mu W[/tex]
The thermal energy generation rate is [tex]91.1\ \mu W[/tex]
