- #1
Karol
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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##