Challenge 1: Alterative way of calculating the flux (bonus 5%).

What is the flux through the area of the circle of the magnetic field of the dipole located in the center of the circle? Of course you may just assume  in (I.11). Use alterative way of calculating this flux - integrate the perpendicular component of the magnetic field over the area of the circle (i.e. either  in (I.8) or  in (I.9) with ). Does your integral converge? Why? Use the property of the magnetic field lines (closed continuous curves) and adjust the limits of your integral to evaluate the flux through the circle.

 

 

Challenge 2: Accelerating magnet (bonus 10%).

Assume the magnet is moving with non-constant velocity. For example, assume the magnet moves with constant acceleration. Does the Model 1 still produce correct estimate for  and magnetic dipole moment ? How about Model 2? Explain. Sketch  signal you expect to see for such accelerating magnet.