Gauss's law in cgs unit system

[Karol]

Homework Statement

Is there a constant parrallel to the ε₀ permittivity in the Gauss law in c.g.s?

Homework Equations

Coulomb force in m.k.s: ##F=\frac{1}{4\pi\varepsilon_0}\frac{qq'}{r^2}##
Coulomb force in c.g.s: ##F=\frac{qq'}{r^2}##
Gauss's law in m.k.s: ##\frac{N}{A}=\varepsilon_0 E##

The Attempt at a Solution

The Coulomb's constant k was transformed to ##\frac{1}{4\pi\varepsilon_0}## in order that the number of field lines N extruding from a surpace round a point charge will equal the net chrage inside the surface:
[tex]\frac{N}{A}=\varepsilon_0 E\rightarrow \frac{N}{4\pi r^2}=\varepsilon_0 \frac{q}{4\pi\varepsilon_0 r^2}\rightarrow N=q[/tex]
So the ##\frac{1}{4\pi}## term was chosen for that in order to cancel with the area of a sphere.
I think, in order that N=q will be also in c.g.s we also need ##\frac{1}{4\pi}## term:
Coulomb's law in c.g.s: ##F=\frac{1}{4\pi B}\frac{qq'}{r^2}\rightarrow \frac{1}{4\pi B}=1##

 

[ehild]

In the cgs system, the Coulomb force is ##F=\frac{q_1 q_2}{r^2} ##,
ε₀=1, D=εE in materials, D=E in vacuum.
Gauss' Law for a single point charge in vacuum ##\oint{E_n dA} = 4\pi q_{enclosed}##

 

[Karol]

I don't know yet this integral.
So i am right, right? Coulomb's law in c.g.s: ##F=\frac{1}{4\pi}\frac{qq'}{r^2}##

 

[ehild]

I don't know yet this integral.
So i am right, right? Coulomb's law in c.g.s: ##F=\frac{1}{4\pi}\frac{qq'}{r^2}##

No. ##F=\frac{qq'}{r^2}##
The electric field around a point charge q is radial, and the magnitude is E=q/r². Integrating is to a sphere of radius r, with the charge in the centre is (4πr²)E = 4πq

 

[HalfLostAndSearching]

I can confirm that there is indeed a constant parallel to the ε0 permittivity in Gauss's law in the cgs unit system. This constant is represented by the value of 1/4π in the cgs version of Coulomb's law. This constant is necessary in order for the number of field lines N to equal the net charge inside the surface, as described in Gauss's law. Without this constant, the equation would not hold true. Therefore, it is important to include this constant in the cgs version of Gauss's law.