Magnetic Force on a Current Carrying Conductor
When a conductor carrying a current is placed inside a magnetic field, it experiences a force. This is known as the motor effect. The direction of the force is at right angles to both the field and the current and can be described by Fleming's Left Hand Rule.
Experiments indicate the forceis proportional to

the magnitude of the magnetic force

the magnitude of the current

The length of the conductorin the magnetic field.

The sine of the angle between the current and the magnetic field.
The magnitude of the force is given byTechnically the force per unit length, in the diagram below is equal to the cross product ofand
It must be noted that ifso that the current and the field are parallel or ifso that current and field are anti – parallel,and the magnetic force is zero. Ifor 270 then current and field are at right angles andand the force is maximum in magnitude.