Consider a circular loop (radius a1) that carries current I1 and is located at the origin. (a) What is B due to this loop at a location on the same plane as the loop and a distance d from this loop (x=0,y=d,z=0)? (Hint: use magnetic dipole formulas and assume d>>a1). (b) if a second circular loop (radius a2 ) is placed at (x=0,y=d,z=0), what is the mutual inductance between the two loops? (Hint: Assume B generated by the first loop is constant over the surface of the second loop). (c) if I1=I0sin(2pi t/T) , where T is the periodicity, what is the voltage induced on the second loop? What is the direction of the current induced (clockwise or counterclockwise with respect to the shown observer) at t=T/8? Extra points (if answered correctly, you get 10 more extra points) (d) Assuming the resistance of the second loop is R and we can ignore its self-inductance, what is the force on the second loop? (e) What is the torque on the second loop