441. Problem 34.37 (RHK) We have to show that, in terms of the Hall electric field E and the current density j, the number of charge carriers per unit volume is given by

Solution: Click For PDF Version The Hall electric field arises so that the net Lorentz force on charge carriers inside a conductor is zero. Let be the drift velocity of charge carriers. The magnetic field is so arranged as to have This condition implies that From this equation, we note that As and are orthogonal, we have The current density j in terms of volume density of charge carriers, n, drift speed,, and charge, e, is We thus have
