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Electromagnetism · undergrad

Electric Potential

A scalar potential whose gradient gives the electrostatic field.

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Electric Potential

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Definition

In electrostatics,

E=−∇ϕ.\mathbf E=-\nabla \phi.

The potential difference is work per unit charge:

Δϕ=−∫ABE⋅dl.\Delta \phi = -\int_A^B \mathbf E\cdot d\mathbf l.

Poisson Equation

Combining with Gauss’s law gives

∇2ϕ=−ρε0.\nabla^2\phi=-\frac{\rho}{\varepsilon_0}.
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