A current loop of arbitrary shape is situated in a uniform magnetic...

The magnetic force on a small current element $d\vec{l}$ is given by $d\vec{F} = I(d\vec{l} \times \vec{B})$.

The net magnetic force on the closed loop is $\vec{F} = \oint d\vec{F} = \oint I(d\vec{l} \times \vec{B})$.

Since the magnetic field $\vec{B}$ is uniform, it is constant over the loop and can be taken outside the integral.

$\vec{F} = I \left( \oint d\vec{l} \right) \times \vec{B}$

For any closed loop, the vector sum of the displacement elements is zero, i.e., $\oint d\vec{l} = 0$.

Thus, $\vec{F} = I(0) \times \vec{B} = 0$.

The net magnetic force on any closed current loop in a uniform magnetic field is always zero.