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

Step-by-step explanation:

FOR CLOSED CIRCUIT LOOP IN A UNIFORM MAGNETIC FIELD

total force F=
`I\oint\vec{ds}*\vec{B}`

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

F=
`I*\vec{B}\oint\vec{ds}`

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

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

therefore,

F=
`I*\vec{B}\oint\vec{ds}`=0