Question

A current carrying circular loop of radius R is placed in a uniform magnetic field `B_(0)` Tesla in x-y plane as shown in figure. The loop carries a current `i = 1A` in the direction shown. Find the torqure acting on the loop

Answer 1

`vec(M) = -pi R^(2) hat(k)`
`vec(B) = B_(0) cos 45^(@) hat(i) + B_(0) sin 45^(@)hat(j)`
`tau = vec(M) xx vec(B)`
`= - pi R^(2) hat(k) xx (B_(0))/(sqrt2) (hat(i) + hat(j))`
`= (pi R^(2) B_(0))/(sqrt2) (hat(i) - hat(j))`