Consider a loop with 50 square turns that is 12 cm on a side and is in a uniform 0.6 T magnetic field. Find the current through a loop needed to create a maximum torque of 9.00 N Â· m.
The maximum torque is when two sides of the loop are parallel with the external field and the other two sides of the loop are perpendicular to the filed. Otherwise if the field is perpendicular to the plane of the loop all the forces on the 4 sides of the loop cancel each other and the total torque is zero.
Force on a side of the loop having one turn is $F0 =(B \times I)*L = B*I*L$ for the two perpendicular sides.
Total force on two sides is $F =2*N*F0 =2*N*B*I*L$
$T = F*(L/2) = N*B*I*L^2$
$I = T/(N*B*L^2) =9/(50*0.6*0.12^2) =20.83 A$