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Problem $2$

A circular loop of wire of radius $r$ has a normal vector of hat$(n)=(0,0,1)$ at time $t=0$ initially before it begins rotating in uniform circular motion in the yz$-$plane with a period of $T$ seconds. A magnetic field vec$(B)=B(b_x,b_y,b_z)$ is present as the loop rotates.

If the loop is connected to an electronic circuit that can be modeled as a resistor with resistance, $R,$ determine the power delivered to the circuit as a function of time.