Consider a rod of a uniform cross-sectional area A and length l. Let n be the number density of charge carriers(free electrons) in it.
Then the total number of mobile charge carriers in it is = nAl. Assume that these charge carriers are under motion with a drift velocity, vd.
In the F = (n A l) q vd × B; here q is the charge of each charge carrier. presence of an external magnetic field B, the force on these charge carriers is
But current density j = n q vd
F = j A l × B
But, j A = I, the electric current in the conductor, then
∴ F = I l x B
i.e. F = (I l B sinθ)
