Electrostatic Constant Written Funny

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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.
 

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No one knows?
 
  • #3
Doc Al
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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"
 
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  • #4
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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
 
  • #5
jtbell
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It's partly for historical reasons, and partly a matter of minimizing the number of equations that have factors of [itex]4 \pi[/itex].

Using [itex]\epsilon_0[/itex] Coulomb's Law is more complicated:

[tex]F_{elec} = \frac {1} {4 \pi \epsilon_0} \frac {q_1 q_2} {r^2}[/tex]

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

[tex]\vec \nabla \cdot \vec E = \frac {\rho} {\epsilon_0}[/tex]

[tex]C = \frac {\epsilon_0 A}{d}[/tex]

Whereas using k, Coulomb's Law is simpler:

[tex]F_{elec} = k \frac {q_1 q_2} {r^2}[/tex]

but you have to insert factors of [itex]4 \pi[/itex] into other equations:

[tex]\vec \nabla \cdot \vec E = 4 \pi k \rho[/tex]

[tex]C = \frac {A}{4 \pi k d}[/tex]
 
  • #6
madmike159
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Well 1/4pi*e0 is where 9x10^9 came from.
 

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