A current loop of arbitrary shape lien in a uniform magnetic field B. show that the net magnetic force acting on the loop is zero.

Explanation

For any current segment of loop of length dl, we can write magnetic force due to external magnetic field `vec B` applied as follows:
` d vecF = id vecl xx vecB`
Here we know that the magnetic field is uniform. We can take `vecB` out of the integration to get the net force. Hence, total force for the loop placed inside the uniform magnetic field can be written as follows:
`vecF = i (underset("loop")int d vecl) xx vecB`
Now we know that the loop is closed and hence integration of `d vecl` must yield were because all segments of the loop are like a closed polygon made out of vectors. Hence, in a uniform majetic field condition, a closed loop of current will experience no net force .