= 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> $\mathbf F=\nabla(\boldsymbol\mu\cdot\mathbf B)$ 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.
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