Storyboard

An electric field is a physical property of space generated by electric charges. It describes how one charge can influence another even at a distance, establishing a direction and intensity of interaction at each point. If a positive charge is placed in a region where an electric field exists, it will tend to move in the direction of the field, while a negative charge will move in the opposite direction.

The electric field allows us to interpret electric forces not as an instantaneous action between separate objects, but as a modification of space produced by charges. In this way, a charge alters the environment around it, and any other charge that enters that region experiences a force determined by the local characteristics of the field.

Electric fields are present in numerous natural and technological phenomena. They participate in the structure of atoms and molecules, in electrical conduction, in the operation of circuits, screens and electronic devices, and even in biological processes related to cell membranes and nerve transmission.

>Model

ID:(814, 'ky')

Description

Once Electric eield ($E$) is known, Electric force ($F$), which acts on Charge ($q$), can be calculated using:

$F = q E$

Variables

$F$

Force with constant mass

$N$

$q$

Load on which the force acts

$C$

$E$

Electric eield

$V/m$

ID:(3872, 'gm')

Description

The magnitude of Electric force ($F$) generated between two charges, represented by Test charge ($q$) and Charge ($Q$), which are located at a distance of Distance ($r$), is calculated using Electric field constant ($\epsilon_0$) and Dielectric constant ($\epsilon$) as follows:

equation=1697

With the definition of the electric field as

equation=15785

is obtained

equation

ID:(11379, 'gm')

Description

Analogously to the calculation of the scalar Electric force ($F$) over Charge ($q$) by multiplying by Electric eield ($E$):

$F = q E$

It is possible to generalize this relationship to the three-dimensional case, calculating Electric force ($\vec{F}$) as the product of Charge ($q$) by the vector electric field Electric field ($\vec{E}$), so that:

$\vec{F} = q \vec{E}$

Variables

$\vec{F}$

Force

$N$

$q$

Test charge

$C$

$\vec{E}$

Electric field

$V/m$

ID:(15811, 'gm')

Description

In a one-dimensional world, the electric field on a test particle is equal to Electric field ($\vec{E}$) generated by Charge ($Q$), located at a distance Distance ($r$) and the direction reflected by Versor ($\hat{n}$). Its magnitude can be calculated using Electric field constant ($\epsilon_0$) and Dielectric constant ($\epsilon$) by:

$\vec{E} =\displaystyle\frac{1}{4 \pi \cdot \epsilon_0 \cdot \epsilon }\displaystyle\frac{ Q }{ r ^2}\hat{n}$

Variables

$r$

Radius

$m$

$\epsilon$

Dielectric constant

$-$

$\hat{n}$

Versor

$-$

$Q$

Charge

$C$

$q$

Charge

$C$

$\vec{E}$

Electric field

$V/m$

$\epsilon_0$

Electric field constant

8.854187e-12

$C^2/m^2N$

ID:(790, 'gm')

Description

Force ($\vec{F}$) on Test charge ($q$) in Position ($\vec{r}$) depend on Number of charges ($N$), accounted for with index $i$, represented by Charge of the ion i ($Q_i$) located in Position of a charge i ($\vec{u}_i$). With the parameters Dielectric constant ($\epsilon$) and Electric field constant ($\epsilon_0$), this can be written as:

equation=10392

With the definition of Electric field ($\vec{E}$) given by

equation=3724

we have that the electric field of a distribution of charges is

equation

ID:(3726, 'gm')

Description

Calculations

• Alternative method
• Traditional method
• Strategy
• 2D
• 3D

Equation

Number

First, select the equation:   to ,  then, select the variable:   to 

---

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

 Variable   Given   Calculate   Target :   Equation   To be used

Variables

$r$

r

Distance between charges

m

$\vec{r}$

&r

Position

m

$\vec{u}_i$

&u_i

Position of a charge i

m

$r$

r

Radius

m

$\epsilon$

epsilon

Dielectric constant

-

$N$

N

Number of charges

-

$\hat{n}$

&n

Versor

-

$\vec{F}$

&F

Force

N

$F$

F

Force with constant mass

N

$q$

q

Charge

C

$Q$

Q

Charge

C

$Q_i$

Q_i

Charge of the ion i

C

$q$

q

Load on which the force acts

C

$q$

q

Test charge

C

$E$

E

Electric eield

V/m

$\vec{E}$

&E

Electric field

V/m

$\epsilon_0$

epsilon_0

Electric field constant

C^2/m^2N

ID:(814, 0)