The concept of Lorentz force can be extended to current carrying conductors placed in uniform magnetic field B. Suppose that the magnetic field is parallel to the plane of paper and a conductor of length ∆L carrying current I is placed normal to the field.
Suppose that the current is flowing downward with a drift velocity vd and hence each free electron constituting the current experiences a Lorentz force,
F = e vd.B
If there are N free electrons in the conductor, the net force on it is given by
F = N e vd B = nA ∆L e vd B
where n denotes the number of free electrons per unit volume. But neAvd = I. Hence
F = I ∆L B
If conductor makes an angle θ with B,then |F| = I ∆L B sinθ. The direction of the force is again given by Fleming’s left hand rule.