The force acting on a current-carrying conductor placed in a magnetic field is,

F = B × I × L

The current I is the rate of flow of charge.

Now, if a charge Q flows in time t then the current I = Q/t.

Hence substituting for I in the above equation, we get,

F = (B × Q × L)/t

Suppose the particle carrying the charge Q travels a length L in time t, then the velocity

v = L/t. So substituting this value, we get

Force on moving charge F = B × Q × v.