# Force on Current carrying Conductor on Magnetic Field

## Force on Current-Carrying Conductor on Magnetic Field

When a conductor carrying a current is placed in a magnetic field, the conductor experiences a magnetic force.

The direction of this force is always right angles to the plane containing both the conductor and the magnetic field and is predicted by Fleming’s Left-Hand Rule.

A conductor consists of a large no. of free electrons. Current on the conductor means drifting of such a free electron in any fixed direction due to the motion of such a free-electron each electron experiences magnetic force and hence conductor itself experiences a magnetic force.

Consider a conductor having length l, cross-section area A in a uniform magnetic field. If n be the number of electrons per unit volume (electron density) and be the drift velocity of an electron having electronic charge e then the current on the conductor is

Due to the motion of electrons on the magnetic field, each electron experiences Lorent’s magnetic force.

The total number of current on the conductor is

The total force experienced by the conductor isSo the force experienced by the conductor is

perpendicular to the plane containing l and B.
Special Case:
we have

F= Bllsin θ   Case-I:
if θ = 90°

F=Bllsin θ          Case-II:
F=Bll                  if θ = 0° or 180

F=Bllsin θ

F=0