A current i is passed through a silver strip of width d and area of cross section A . The number of free electrons per unit volume is n . A magnetic field B exists perpendicular to the plane of the strip. What will be the potential difference developed across the width of the conductor due to the electron accumulation? (The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is

Step-by-step solution

The relation between current i and drift velocity v_d is given by: i = n e A v_d where e is the elementary charge. Rearranging for v_d , we get: v_d = i n e A The magnitude of the magnetic force F_m on a single free electron moving with drift velocity v_d in a perpendicular magnetic field B is: F_m = e v_d B Substituting the expression for v_d into the force equation: F_m = e ( i n e A ) B = i B n A To find the direction, note that the current i flows to the right, which means the free electrons drift to the left.