It has been observed that when an current carrying conductor is placed inside an magnetic field, the conductor is experienced a force in the direction perpendicular to both direction of current and direction of magnetic flux.
In the figure, a conductor lying vertically in a uniform horizontal magnetic field of strength H. If l is the length of the conductor tying within this magnetic field and i is the current through it, then the force experienced by the conductor will be
F = B.i.l Newton
= μ0.μr.H.i.l Newton
The direction of the force F can also be determined by Flemming's Left Hand Rule. As per this rule, if any one holds out his or her hand with fore finger, second finger and thumb at right angle to each other, then his or her fore-finger will indicate the direction of magnetic field, the second finger will indicate the direction of flow of current and the thumb will give the direction of force or motion of the conductor.
So far we have discussed about the force experienced by a current carrying conductor placed in perpendicularly in the field. The conductor inside the field may lie at an angle θ with the field. Then field strength H can be resolved in two components Hcos(θ) parallel to the conductor and Hsin(θ) perpendicular to the conductor. In this case the force experienced by the conductor will be
F = B.i.l.sin(θ) Newton.