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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 82254.png, where82247.png= current element, 82260.png.
Fig. 23
Total magnetic force, 82182.png.
If magnetic field is uniform, i.e., 82188.png = constant, then 82194.png.
82200.png 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 82206.png joining initial to final point.
(For a straight conductor F = Bil sin θ)

Direction of force

The direction of force is always perpendicular to the plane containing 82212.png and is same as that of the cross-product of two vectors 82220.png with 82231.png (Fig. 24).
Fig. 24
The direction of force when current element 82240.png and 82277.png are perpendicular to each other can also be determined by applying either of the following rules

Fleming’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 82283.png 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 82289.png and thumb in the direction of current i, then normal to the palm will point in the direction of force (Fig. 26).

Fig. 26

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