# Electrostatic Constant Written Funny

• Pupil
In summary, the electrostatic constant k can be written as either 9*10^9 or 1/(4*pi*e0). This is because e0, or the electric permittivity of free space, is a constant that is used in equations involving electric fields and charges. It is used to simplify equations such as Coulomb's Law and the parallel-plate capacitor equation. While using k may make some equations simpler, it also requires the insertion of factors of 4*pi in other equations. Overall, both forms of the electrostatic constant are used for different reasons, but they are ultimately equivalent.

#### Pupil

So the electrostatic constant k = 9*10^9, but I've also seen it written in my Fundamentals of Phys book (Resnick) and Wikipedia as k = 1/(4*pi*e0). Why is this? Thanks.

No one knows?

Pupil said:
So the electrostatic constant k = 9*10^9, but I've also seen it written in my Fundamentals of Phys book (Resnick) and Wikipedia as k = 1/(4*pi*e0). Why is this? Thanks.
The ε0 is a constant called the electric permittivity of free space. Read about it here: http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/elefie.html#c3"

Last edited by a moderator:
The capacitance of a parallel plate air capacitor of area A and plate separation d is

C = e0 A/d

where the permittivity of free space e0 = 1/(u0 c2) = 8.85 x 10-12 Farads per meter,
and the permeability of free space is
u0 = 4 pi x 10-7 Henrys per meter

It's partly for historical reasons, and partly a matter of minimizing the number of equations that have factors of $4 \pi$.

Using $\epsilon_0$ Coulomb's Law is more complicated:

$$F_{elec} = \frac {1} {4 \pi \epsilon_0} \frac {q_1 q_2} {r^2}$$

but other equations like Gauss's Law and the parallel-plate capacitor equation are simple:

$$\vec \nabla \cdot \vec E = \frac {\rho} {\epsilon_0}$$

$$C = \frac {\epsilon_0 A}{d}$$

Whereas using k, Coulomb's Law is simpler:

$$F_{elec} = k \frac {q_1 q_2} {r^2}$$

but you have to insert factors of $4 \pi$ into other equations:

$$\vec \nabla \cdot \vec E = 4 \pi k \rho$$

$$C = \frac {A}{4 \pi k d}$$

Well 1/4pi*e0 is where 9x10^9 came from.

## 1. What is the electrostatic constant?

The electrostatic constant, also known as the vacuum permittivity or electric constant, is a physical constant that relates the strength of an electric field to the magnitude of electric charges in a vacuum.

## 2. How is the electrostatic constant measured?

The electrostatic constant is measured by calculating the force between two stationary charged particles in a vacuum, and then dividing that force by the product of the charges and the square of the distance between them.

## 3. What is the value of the electrostatic constant?

The value of the electrostatic constant is approximately 8.854 x 10^-12 farads per meter (F/m) in the International System of Units (SI).

## 4. Why is the electrostatic constant important?

The electrostatic constant is an important fundamental constant in electromagnetism and plays a crucial role in understanding the behavior of electric charges. It is also used in many practical applications, such as in the design of electronic devices and in the study of electrostatic phenomena.

## 5. How does the electrostatic constant relate to Coulomb's law?

Coulomb's law, which describes the force between two stationary charged particles, includes the electrostatic constant as a proportionality constant. This means that the electrostatic constant determines the strength of the force between charged particles in a vacuum.