Formula: Plate capacitor Electric potential Position Voltage Plate distance

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

Rearrange formula

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.

Related formulas

Plate Capacitor (Force, Voltage, Charge, Distance)

$$ F ~=~ \class{red}{q} \, \frac{U}{d} $$

Plate Capacitor (Capacitance)

$$ C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d} $$

Plate Capacitor (Energy, Electric Field)

$$ W_{\text{e}} ~=~ \frac{1}{2} \, \varepsilon_0 \, \varepsilon_{\text r} \, V \, \class{purple}{E}^2 $$

Plate Capacitor (Electric Field, Voltage, Distance)

$$ \class{purple}{E} ~=~ \frac{U}{d} $$

Capacitor (Energy, Capacitance, Charge)

$$ W_{\text{e}} ~=~ \frac{1}{2} \, \frac{Q^2}{C} $$

Capacitor (Energy, Voltage, Capacitance)

$$ W_{\text e} ~=~ \frac{1}{2} \, C \, U^2 $$

Plate Capacitor (Attraction Force, Voltage)

$$ F ~=~ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2d^2}\, U^2 $$

Plate Capacitor (Attraction Force, Charge)

$$ F ~=~ \frac{Q^2}{2\varepsilon_0 \, \varepsilon_{\text r} A} $$

Plate Capacitor: Voltage, Capacitance and Eletric Force

Here the plate capacitor is simply explained. With the help of the capacitor you will learn about the electric voltage, electric field and electric capacitance and how to calculate them for a plate capacitor.

Derivations & Experiments

Plate Capacitor: Potential, E-field, Charge and Capacitance

Here, the electrostatic potential, electric field and the capacitance of a plate capacitor are derived using Laplace's equation.

Exercises with solutions

Create a Plate Capacitor with a Certain Capacitance

In this exercise (with solution) you have to calculate the distance between the capacitor plates for a given capacitance and and than use relative permittivity.

Charge in a thundercloud

The exercise teaches you how to calculate the charge of a thundercloud using the capacitance and E-field in the plate capacitor.

Capacitor with and without dielectric in comparison

In this exercise with solution about the plate capacitor, the capacitance, voltage and energy must be compared with and without dielectric.

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