# Maximum torque of the field on current loop

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 $F =2*N*F0 =2*N*B*I*L$

Torque is

$T = F*(L/2) = N*B*I*L^2$

$I = T/(N*B*L^2) =9/(50*0.6*0.12^2) =20.83 A$