My name is Alexander FufaeV and here I write about:

What are Equipotential Lines?

Important Formula

Formula: Plate capacitor

$$\varphi_x = - \frac{U}{d} \, x ~+~ \varphi_1$$ $$\varphi_x = - \frac{U}{d} \, x ~+~ \varphi_1$$ $$\varphi_1 = \varphi_x + \frac{U}{d} \, x$$ $$x = \frac{d \, (\varphi_1 - \varphi_x) }{U}$$ $$U = \frac{d \, (\varphi_1 - \varphi_x) }{x}$$ $$d = \frac{U}{ \varphi_1 - \varphi_x } \, x$$

Rearrange formula

What do the formula symbols mean?

Electric potential

$$ \varphi_x $$ Unit $$ \frac{\mathrm{J}}{\mathrm{C}} $$

Electric potential between capacitor plates increases linearly with distance $x$ from one plate to the other.

Electric potential

$$ \varphi_1 $$ Unit $$ \frac{\mathrm{J}}{\mathrm{C}} $$

Electric potential at the location of the capacitor plate that has the greater potential.

Position

$$ x $$ Unit $$ \mathrm{m} $$

Any position within the plate capacitor where the potential $\varphi_x$ is measured.

Voltage

$$ U $$ Unit $$ \mathrm{V} $$

Voltage between the two capacitor plates.

Plate distance

$$ d $$ Unit $$ \mathrm{m} $$

Distance between the capacitor plates.

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.

What is an equipotential line?

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.

Example: Equipotential lines inside a plate capacitor

Example of equipotential lines with potentials $\varphi_0$ to $\varphi_5$ of a homogeneous electric field.

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.