 Magnetic field gradient

A magnetic field gradient describes how a magnetic field varies with position. Because the field is a vector field, its complete local variation is the tensor with components $\partial B_i/\partial x_j$; the gradient of the field magnitude is a different, vector-valued quantity.

A fixed magnetic dipole moment in a nonuniform field experiences a force $\mathbf{F}=\nabla (\mathbf{\mu }\cdot \mathbf{B})$ in the simple localized-dipole model. A uniform field can exert a torque without that translational force. This distinction underlies spatial separation in the Stern-Gerlach experiment and forces in magnetic tweezers. Measuring the field at neighboring positions tests a gradient; one field reading cannot determine it.