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Electric Field Gradient

The electric field gradient is a crucial factor influencing analyte migration, particularly in complex electrophoresis systems, affecting separation efficiency.
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The statement of the theorem

Let E(x,t)\mathbf{E}(\mathbf{x}, t) be the electric field vector at position x\mathbf{x} and time tt. The electric field gradient is mathematically represented by the gradient tensor ∇E\nabla \mathbf{E}, whose components are the partial derivatives of the field components: \n∇E=[∂Ei∂xj]i,j=13\nabla \mathbf{E} = \left[ \frac{\partial E_i}{\partial x_j} \right]_{i, j=1}^3 \nThis tensor quantifies how the electric field varies spatially.