Question

2. Show that the total force on a closed circuit carrying a current I in a uniform magnetic field is zero. The circuit is made of thin wires.

Answer 1

Explanation:

FOR CLOSED CIRCUIT LOOP IN  A UNIFORM MAGNETIC FIELD

total force F= $I\oint\vec{ds}\times\vec{B}$

here vector B has constant strength and direction so, we take it outside the integral

F= $I\times\vec{B}\oint\vec{ds}$

$\oint\vec{ds}$= This vector displacements yields overall displacement

so, $\oint\vec{ds}$=0

therefore,

F= $I\times\vec{B}\oint\vec{ds}$=0