Electrostatic forces and fields - SimuFísica

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Loads = 2

Load values

q₁ = 1 μC

q₂ = -1 μC

q₃ = 1 μC

q₄ = -1 μC

Show grid

Adjust. loads to us

Strengths

Fields

Show strength

q₁

q₂

q₃

q₄

Force values

Resultant forces

Parallelogram rule

Force values

Module

Unit vectors

F₁₂ = N

F₂₁ = N

F₁₃ = N

F₃₁ = N

F₁₄ = N

F₄₁ = N

F₂₃ = N

F₃₂ = N

F₂₄ = N

F₄₂ = N

F₃₄ = N

F₄₃ = N

Modules das forças resultantes:

F₁ = N

F₂ = N

F₃ = N

F₄ = N

$\vec{F}_{12} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{21} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{13} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{31} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{14} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{41} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{23} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{32} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{24} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{42} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{34} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{43} =$

$\hat{i}$

$\hat{j}$ N

Forças resultantes:

$\vec{F}_{1} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{2} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{3} =$

$\hat{i}$

$\hat{j}$ N

$\vec{F}_{4} =$

$\hat{i}$

$\hat{j}$ N

Show electric field

Electric field

Electric field

Normalized field

Lines of force

Field at one point

Show values

Show fields

Show resulting field

Parallelogram rule

Electric field values

Module

Unit vectors

E₁ = N/C

E₂ = N/C

E₃ = N/C

E₄ = N/C

E_R = N/C

$\vec{E}_1 =$

$\hat{i}$

$\hat{j}$ N/C

$\vec{E}_2 =$

$\hat{i}$

$\hat{j}$ N/C

$\vec{E}_3 =$

$\hat{i}$

$\hat{j}$ N/C

$\vec{E}_4 =$

$\hat{i}$

$\hat{j}$ N/C

$\vec{E}_R =$

$\hat{i}$

$\hat{j}$ N/C

Information

This app shows the electrostatic forces and fields generated by point charges.

Use the mouse or the usual touchscreen gestures:

With one finger, or the mouse arrow, hold and drag to move the loads into place.

Buttons:

Enables or disables the reference grid.
Shifts loads to the nearest grid node.
: Accesses various application settings.

The application operates in two modes: forces and fields.

In forces mode, it is possible to visualize all electrostatic forces acting between charges, as well as the resulting forces and their values.
In fields mode, it is possible to visualize, throughout space, the electric field produced by charges. It is also possible to visualize the lines of force and the electric field vector at a specific point, as well as the resulting field.

Version:1.9 (14/07/2024)

How to quote this software?

Marco P. M. de Souza, Electrostatic forces and fields - SimuFísica. Access at 26/07/2025 [Online]. Available at: https://simufisica.com/en/electrostatic-forces-fields/.

Additional details

The electrostatic force on charge $q_i$ , due to the influence of all other charges, is given by

$\overrightarrow{F}_{ij} = \sum_{j \neq i}^N \dfrac{k q_i q_j}{r_{ij}^2}\hat{r}_{ij},$

where

$N$ : number of loads
$k = 9\times 10^9$ : electrostatic vacuum constant.
$\overrightarrow{r}_{ij}$ : vector that starts from charge $q_j$ and ends at charge $q_i$ .

Similarly, the electric field generated by the $N$ charges in the position vector $\overrightarrow{r}$ of space, with each of them located in the position vectors $\overrightarrow{R}_i$ , is given by

$\overrightarrow{E}(\overrightarrow{r}) = \sum_{i=1}^N \dfrac{k q_i}{ \left| \overrightarrow{r} - \overrightarrow{R}_i \right|^3 }(\overrightarrow{r} - \overrightarrow{R}_i)$

Read more:

H. Moysés Nussenzveig, Curso de Física Básica: Eletromagnetismo (Blucher, 2013).

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Electric dipole
Electric quadrupole (linear)
Electric quadrupole (nonlinear)

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