# Force on a Current-Carrying Conductor in Magnetic Field

In case of a current-carrying conductor in a magnetic field, the force experienced by its small length element is given as , where= current element, .

**Fig. 23**

Total magnetic force, .

If magnetic field is uniform, i.e., = constant, then .

is the vector sum of all the length elements from initial to final point. Which is in accordance with the law of vector addition and is equal to the length vector joining initial to final point.

(For a straight conductor

*F*=*Bil*sin*Î¸*)# Direction of force

The direction of force is always perpendicular to the plane containing and is same as that of the cross-product of two vectors with (Fig. 24).

**Fig. 24**

The direction of force when current element and are perpendicular to each other can also be determined by applying either of the following rules

# Flemingâ€™s left hand rule

Stretch the fore finger, central finger, and thumb of left hand mutually perpendicular. Then if the fore finger points in the direction of field and the central in the direction of current

*i*, the thumb will point in the direction of force (Fig. 25).**Fig. 25**

# Right-hand palm rule

Stretch the fingers and thumb of right hand at right angles to each other. Then if the fingers point in the direction of field and thumb in the direction of current

*i*, then normal to the palm will point in the direction of force (Fig. 26).**Fig. 26**