電磁気学 · 学部

Electric Potential

A scalar potential whose gradient gives the electrostatic field.

公開 2026年4月26日 · 1 分

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Definition

In electrostatics,

\mathbf E=-\nabla \phi.

The potential difference is work per unit charge:

\Delta \phi = -\int_A^B \mathbf E\cdot d\mathbf l.

Combining with Gauss’s law gives

\nabla^2\phi=-\frac{\rho}{\varepsilon_0}.

Electric flux through a closed surface measures the enclosed charge.

電磁気学の四本柱。微分形・積分形・共変形をひとつの俯瞰で。