Question

can someone show me why
1 statcoulomb=3.3356*10^(-10) C

Answer 1

In cgs units coulomb force is measured in dynes and charge in statcoulombs.
In mks units coulomb force is measured in newtons and charge in coulombs.

10^5 dynes = 1 newton

writing coulombs law
\[ F =10^{5 }*8.987 *10^{9} Q _{c}^{2}/D ^{2}(m) \] writing out all the dimensions in mks we get

Nt*m^2/C^2

In cgs unit

F= q^2/d^2 dynes*cm^2/statcoul^2

set F in cgs = F in mks

q^2/d^2 = 8.987*10^9*Q^2/D^2

Thus equating the units

Dynes cm^2/statcoul^2= 8.987*10^9*NT*m^2/coul^2


let k=coul/statcoul ;100cm =1m: 1Nt=10^5dynes

Dynes*.0001m^2/statcoul^2 = 8.897*10^9*10^5*dynes*m^2/(k*statcoul)^2

thus k^2 = 8.987*10^9*10^9 and k = 2.9827*10^9

Thus q = Q/k = 3.3356*10^-10

Answer 2

You can't imagine how many times I stumbled in this response.