Question

suppose that the magnetic field in some region has the form B=kzx. Find the force on a square loop lying in yz plane and centered at origin. if it carries a current I, flowing counterclockwise when you look down the x axis

Answer 1

suppose current is flowing through the loop in counterclockwise direction.

force on the left side of square cancels with the force on the right side

the force on the top is

IaB = I a k($\frac{a}{2})$ = Ik $\frac{a^{2}}{2}$ (direction is upward)

similarly, the force on the bottom is IaB = - I a k($\frac{a}{2}$ ) = -Ik $\frac{a^{2}}{2}$ (upward)

The net force is F = Ika$^{2} \hat{\ z}$