JEE Main & Advanced Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Force On a Current Carrying Conductor In Magnetic Field

In case of current carrying conductor in a magnetic field force experienced by its small length element is \[d\overrightarrow{F}=id\overrightarrow{l\,}\times \overrightarrow{B}\];  \[id\overrightarrow{l\,}\]= current element \[d\overrightarrow{F}=i(d\overrightarrow{l\,}\times \overrightarrow{B})\]

Total magnetic force \[\overrightarrow{F}=\int{d\overrightarrow{F}}=\int{i(d\overrightarrow{l\,}\times \overrightarrow{B})}\]. If magnetic field is uniform i.e., \[\overrightarrow{B}=\] constant \[\overrightarrow{F}=i\,[\int{\overrightarrow{dl}}]\times \overrightarrow{B}=i(\overrightarrow{L}\times \overrightarrow{B})\]

\[\int_{{}}^{{}}{\overrightarrow{dl}}=\overrightarrow{L}'=\] vector sum of all the length elements from initial to final point. Which is in accordance with the law of vector addition is equal to length vector \[\overrightarrow{L}\] joining initial to final point.

(For a straight conductor \[F=Bil\sin \theta \])

Direction of force : The direction of force is always perpendicular to the plane containing \[i\overrightarrow{dl}\] and \[\overrightarrow{B}\] and is same as that of cross-product of two vectors \[(\overrightarrow{A}\times \overrightarrow{B})\] with \[\overrightarrow{A}=i\,\overrightarrow{dl}\].

The direction of force when current element \[i\,\overrightarrow{dl}\] and \[\vec{B}\] 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 \[\overrightarrow{B}\] and the central in the direction of current i, the thumb will point in the direction of force.

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 \[\overrightarrow{B}\] and thumb in the direction of current i, then normal to the palm will point in the direction of force