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 drift velocity of the free electrons is v_d . The current i flowing through the strip is given by: i = n e A v_d v_d = i n e A When the magnetic field B is applied perpendicular to the current, the electrons experience a magnetic force: F_m = e v_d B This force causes electrons to accumulate on one side of the strip, setting up a transverse electric field E . In the steady state, the electric force balances the magnetic force: e E = e v_d B E = v_d B The potential difference V developed across the width d of th