As you know, the magnetic north pole of the earth does not coincide with the geographic North Pole--in fact, it's off by about 11^o. Relative to the fixed axis of rotation therefore, the magnetic dipole moment vector of the earth is changing with time, and the earth must be giving off magnetic dipole radiation. 

(a) Find the formula for the total power radiated, in terms of the following parameters: ψ (the angle between the geographic and magnetic north poles), M (the magnitude of the earth's magnetic dipole moment), and co (the angular velocity of rotation of the earth). 

(b) Using the fact that the earth's magnetic field is about half a gauss at the equator, estimate the magnetic dipole moment M of the earth. 

(c) Find the power radiated.  

(d) Pulsars are thought to be rotating neutron stars, with a typical radius of 10 km, a rotational period of 10^-3s, and a surface magnetic field of 10⁸ T What sort of radiated power would you expect from such a star?