What are Equipotential Lines?
An equipotential line (or in three-dimensional space: equipotential surface) is the set of all points in space that have the same potential \(\varphi\). A potential \(\varphi \) is potential energy per charge.
An equipotential line is a line on which the potential energy of a charge is constant.
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.
A plate capacitor (see illustration) generates a homogeneous electric field \(\class{purple}{E}\). 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.
