Two parallel conducting rails with negligible resistance are connected at one end by a resistor of resistance R. The rails are placed in a magnetic field Bext, which is perpendicular to the plane of the rails. This magnetic field is uniform and time independent. The distance between the rails is L. A conducting rod slides without friction on top of the two rails at constant velocity,v.
a) Using Faraday's Law of Induction, calculate the magnitude of the potential difference induced in the moving rod.
b) Calculate the magnitude of the induced current in the rod,iind.
c) Show that for the rod to move at a constant velocity as shown, it must be pulled with an external force,Fext, and calculate the magnitude of this force.
d) Calculate the work done, Wext, and the power generated, Pext, by the external force in moving the rod.
e) Calculate the power using (dissipated) by the resistor, Pr. Explain the correlation between this result and those of part (d).