# Magnetic Force

## What is Magnetic Force

### Force on a Current Carrying Wire due to  Magnetic Field :

Introduction : A current carrying conductor produces a magnetic field around it. When it is placed in a magnetic field, the two magnetic fields interact. A force acts on the conductor.

Expression : It is found by calculation that if the conductor of, length l be carrying a current I lying inside a magnetic field of intensity B and making an angle q with it, the force acting on it is given by

F = Il B sin θ

### Fleming’s Left–Hand Rule

Fleming’s left–hand rule is used to find out the direction of motion of a current–carrying conductor when placed in a magnetic field. This rule states as follows.

Stretch out the thumb, the forefinger, and the second (middle) finger of the left hand so that these are at right angles to each other. If the forefinger gives the direction of the magnetic field (N to S), the second (middle) finger  the direction of current (+ to –), then the thumb gives the direction of the force acting on the conductor.

Since the conductor will move in the direction of the force acting on it hence the thumb gives the direction of motion of the conductor.

### Force on a moving charge

A current–carrying conductor (e.g., a wire) experiences a force when placed in a magnetic field. The current represents a collection of charged particles in motion. Therefore, each moving charged particle in a magnetic field will also experience a force, called Lorenz force.

The direction of the force experienced by a positive charge is the same as that on the current and is given by Fleming’s left-hand rule.

The force, experienced by a current carrying conductor in a magnetic field is given by,

F = B I l

If Q is the charge passed through the conductor in time t, we can write

I = $\frac{Q}{t}$

The above relationships, when combined give,

F = $\frac{{BQ\ell&space;}}{t}$ = BQv

where v is the velocity of the charged particle perpendicular to the direction of the field