Electric Field from VoltageOne of the values of calculating the scalar electric potential (voltage) is that the electric field can be calculated from it. The component of electric field in any direction is the negative of rate of change of the potential in that direction.
For rectangular coordinates, the components of the electric field are

Index Voltage concepts Electric field concepts  

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Electric Field as GradientThe expression of electric field in terms of voltage can be expressed in the vector form This collection of partial derivatives is called the gradient, and is represented by the symbol ∇ . The electric field can then be written Expressions of the gradient in other coordinate systems are often convenient for taking advantage of the symmetry of a given physical problem. 
Index Electric field concepts Voltage concepts  

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