CBSE Class 12 · 2024 · Magnetic Effects of CurrentShort Answer

Consider the conductor carrying current $I$ with $n$ free charge carriers per unit volume, each of charge $e$ drifting with velocity ${\vec{v}}_d$, and cross-sectional area $A$.
The force on one carrier is $e{\vec{v}}_d\times \vec{B}$, and the number of carriers in length $L$ is $nAL$, so the total force is

Using $I=neA{v}_d$ and writing $\vec{L}$ in the direction of current flow,

For a zig-zag (bent) conductor, the force must be found by adding $Id\vec{\ell }\times \vec{B}$ over all elements. For a uniform $\vec{B}$ this sum reduces to $I\vec{L}\times \vec{B}$ where $\vec{L}$ is the straight vector joining the two end points, so the magnitude is generally smaller than $BIL$ and can even be zero if the conductor forms a closed loop.