Introduction to Electrodynamics · Problem 5.4

The key is recognizing that a non-uniform magnetic field exerts different forces on opposite sides of the loop, so they don't cancel—only the net force survives. Since $\mathbf{B}$ varies with $z$, the top and bottom segments of your square loop experience different field strengths. You'll use $\mathbf{F} = I\mathbf{L} \times \mathbf{B}$ for each segment, then add them up to find which direction the loop is pulled.

The key is recognizing that a non-uniform magnetic field exerts different forces on opposite sides of the loop, so they don't cancel—only the net force survives. Since $\mathbf{B}$ varies with $z$, the top and bottom segments of your square loop experience different field strengths. You'll use $\mathbf{F} = I\mathbf{L} \times \mathbf{B}$ for each segment, then add them up to find which direction the loop is pulled.