- #1
mbond
- 41
- 7
The Bohr magneton is (see e.g. Wikipedia) in SI units:
$$\mu_B=\frac{e\hbar}{2m_e}$$
and in CGS units:
$$\mu_B=\frac{e\hbar}{2m_ec}$$
So the dimension of the electric charge in SI, ##[q_{SI}]##, is related to the dimension of the electric charge in CGS, ##[q_{CGS}]##, by:
$$[q_{CGS}]=[q_{SI}].velocity$$
Now, the electrostatic force between two charges ##q_1## and ##q_2## separated by a distance ##r## is in SI:
$$F=\frac{q_1q_2}{4\pi\epsilon_0r^2}$$
and in CGS:
$$F=\frac{q_1q_2}{r^2}$$
So the dimension of the permitivity, ##[\epsilon_0]##, is given by:
$$[\epsilon_0]=\frac{[q_{SI}]^2}{[q_{CGS}]^2}=velocity^{-2}$$
which is not true.
So I guess I make a mistake somewhere, and I would be grateful for any help.
$$\mu_B=\frac{e\hbar}{2m_e}$$
and in CGS units:
$$\mu_B=\frac{e\hbar}{2m_ec}$$
So the dimension of the electric charge in SI, ##[q_{SI}]##, is related to the dimension of the electric charge in CGS, ##[q_{CGS}]##, by:
$$[q_{CGS}]=[q_{SI}].velocity$$
Now, the electrostatic force between two charges ##q_1## and ##q_2## separated by a distance ##r## is in SI:
$$F=\frac{q_1q_2}{4\pi\epsilon_0r^2}$$
and in CGS:
$$F=\frac{q_1q_2}{r^2}$$
So the dimension of the permitivity, ##[\epsilon_0]##, is given by:
$$[\epsilon_0]=\frac{[q_{SI}]^2}{[q_{CGS}]^2}=velocity^{-2}$$
which is not true.
So I guess I make a mistake somewhere, and I would be grateful for any help.