Question

Show that force on a closed circuit in a magnetic field is zero.

Answer 1

If `vecB` is uniform over the whole wire,

`vecF_m = I[vec(dl)] xx vecB`

The above equation can be extended to a closed wire circuit C.

`vecF_m = oint_c Ivec(dl) xx vecB`

Here, the integral is over the closed circuit C for uniform `vecB.`

∴ `vecF_m = [oint_c I vec(dl)] xx vecB`

Where

`oint_c vec(dl)` = sum of the vectors along a closed = 0

∴ `vecF_m = 0 ("if"  vecB  "is uniform")`