Question

Obtain the expression for force acting on the current conductor in magnetic field. Give the right hand palm rule for the direction of this force.

Answer 1

Consider a conductor of area of cross section A and lengths ${}^{\prime }{l}^{\prime }$ placed in a uniform magnetic field.. Let ${}^{\prime }{n}^{\prime }$ be the no of free $\overline{e}$ per unit volume of the conductor.

$F=q(\overrightarrow{v_d}\times \overrightarrow{B})$

$v_d\to$ drift velocity

Total no of $\overline{e}$ in the conduction

$=Volume\times n$

$=Aln$

Total charge = $Alne$

Force on the conduction

$F=q(\overrightarrow{v_d}\times \overrightarrow{B})$

$v_d\to$ drift velocity

$F=Alne(\overrightarrow{v_d}\times \overrightarrow{B})$

$=Ane{V}_d(\overrightarrow{l}\times \overrightarrow{B})$

$=I(\overrightarrow{l}\times \overrightarrow{B})$

$F=I(\overrightarrow{l}\times \overrightarrow{B})$

The right hand rule states that, to find the direction of magnetic forces on a positive moving change, the thumb of the right hand point is the direction of v the fingers is the direction of $B$, and the force is directed perpendicular to the right hand palm