# Force on A Current-Carrying Conductor in A Uniform Magnetic Field

When a conductor is carrying the current and it is placed in the magnetic field then a magnetic force is experienced by the conductor. The direction of this acting force is always right angles to the plane that is containing both the magnetic field and the conductor.

Concerning the above diagram, F is denoting the force and B is showing the magnetic field, while I represent the current. There are some factors which affect the magnetic force on the current-carrying conductor in the magnetic field. These factors include the length of wire, the amount of current that is flowing through the wire, and the strength of the magnetic field.

The conductor has a huge number of electrons, and the current in the conductor means the drifting of free electrons in any of the fixed direction, as each electron experiences the magnetic force due to the motion of free electrons. Resultantly the magnetic force is also experienced by the conductor. Let consider the conductor that is having the length l and cross-sectional area A and is placed in the uniform magnetic field If n is the number of electrons that are present per unit volume, and Vd is the drift velocity of the electrons that are having the electronic charge e, then the current in the conductor can be represented as follows.

Due to the movement of electrons in the magnetic field, the Lorentz magnetic force is experienced by each electron.

The total current on the conductor can be represented as below.

The total force that is experienced by the conductor is as following.

It can be said that the force which is experienced by the conductor is perpendicular to the plane that is containing I and B.

## Direction of Force

The direction of the force on the current-carrying conductor that is placed in the magnetic field can be found by Fleming’s left-hand rule. The middle finger, forefinger, and thumb of the left hand are stretched in the mutually perpendicular direction. If the forefingers are pointing in the direction of the magnetic field and middle finger is pointing in the direction of the current, then the thumb points the direction of the force that is acting on the conductor.

## Magnitude of Force

The magnitude of the force can be represented by using a given formula.

F = BIl sin θ

If the conductor is placed in the perpendicular direction to the magnetic field then it experiences the maximum force and if it is placed in the parallel direction along the magnetic field then the force is zero.