# What is the total force on any arbitrary current carrying loop in a uniform magnetic field ? Prove your answer

Sep 18, 2015

The force is zero.

#### Explanation:

The force on a current carrying wire moving in a uniform magnetic field $B$ is given by:

$F = I \left(B \times L\right)$

The direction of the vector $L$ is the same as the direction of the current through the wire $\left(I\right)$.

If the wire is a closed loop then vector $L$ starts and finishes at the same place so is zero.

So:

$F = I \left(B \times 0\right) = 0$