Two parallel conducting (negligible resistance) frictionless rails are connected at one end by a resistor R. The rails are placed in a magnetic field, B which is perpendicular to the plane of the rails. The magnetic field is uniform and constant in time. The distance between the rails is L and a conducting rod slides on top of the two rails with a constant velocity v.

(a) Using Faraday's law derive the equation for the magnitude of the potential difference induced in the moving rod.

(b) Determine the induced current in the rod.

(c) Calculate the force F, that is required to keep the rod moving at a constant velocity.

(d) Calculate the power dissipated in the resistor.