Encyclopedia of Electrical Engineering

A current-carrying conductor produces a magnetic field around it. i.e. behaves like a magnet and exerts a force when a magnet is placed in its magnetic field. Similarly, a magnet also exerts equal and opposite force on the current-carrying conductor. The direction of this force can be determined using Fleming's left-hand rule.
#### Magnetic Force on a single Current-Carrying Conductor

Electric current is an ordered movement of charge. Because charges ordinarily cannot escape a conductor, the magnetic force on charges moving in a conductor is transmitted to the conductor itself. A current-carrying wire in a magnetic field must, therefore, experience a force due to the field.
**Fig.no.1: **Force on a current-carrying conductor.
Now, we are going to involve current $I$ and length $l$ of the wire instead of charge $q$ and velocity $v_d$. hence
$n q (v_d) = nq (l/t) = nq/t (l) = I l$, the above equation will become
$$\bbox[5px,border:1px solid red] {\color{blue}{F=I.l.B \sin\phi}} \tag{1}$$
Where F is force acting on a current carrying conductor, B is magnetic flux density (magnetic field strength), I is magnitude of current flowing through the conductor, l is length of conductor, $\phi$ is angle that conductor makes with the magnetic field.
When the conductor is perpendicular to the magnetic field, the force will be maximum. When it is parallel to the magnetic field, the force will be zero.
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.