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What are Equipotential Lines or Equipotential Surfaces?

Answer #1

Level 2 (without higher mathematics)
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Equipotential Lines of a Homogeneous E-Field of a Plate Capacitor
Example of equipotential lines with potentials \(\varphi_0\) to \(\varphi_5\) of a homogeneous electric field.

An equipotential line (or in 3d: equipotential surface), is the set of all points in space that have the same potential \(\varphi\). A potential \(\varphi\) is potential energy per charge.

What is an equipotential line?

An equipotential line is a line on which every point has the same potential energy.

When a particle moves on such an equipotential line, its potential energy does not change. In other words, the particle on an equipotential line is neither accelerated nor decelerated and it can be moved on the equipotential line without losing or gaining energy.

Example: Equipotential lines of a plate capacitor

A plate capacitor (see illustration) generates a homogeneous electric field \(E\). The equipotential lines are perpendicular to the electric field lines. In the illustration, six equipotential lines (from \(\varphi_0\) to \(\varphi_5\)) are shown as examples. If a charged particle is moved along the equipotential line \(\varphi_2\), for example, then its potential energy will not change.