## Main Question or Discussion Point

It is a well known fact that, in electromagnetic units, strength of a shell and strength of current flowing through its boundary are same. See here.

\begin{equation}
\begin{matrix}
\text{i.e.}\: i \text{(biot)} = \phi \text{(biot) }
\end{matrix}
\tag{1}
\end{equation}

(a) While converting to SI:

\begin{equation}
\begin{matrix}
i\: \text{biot} = i\: (10 \text{Amp}) = 10i\: \text{Amp} = I \text{Amp}\\
\text{where biot} = 10 \text{Amp and}\: 10i = I
\tag{a}
\end{matrix}
\end{equation}
Also:
\begin{equation}
\begin{matrix}
\phi\: \text{biot} = \phi\: (10 \text{Amp}) = 10\phi\: \text{Amp} = \Phi \text{Amp}\\
\text{where biot} = 10 \text{Amp and}\: 10\phi = \Phi
\tag{b}
\end{matrix}
\end{equation}

Therefore in SI (by comparing with equation (1)):

$I$ (Amp) = $\Phi$ (Amp)

(b) While converting to electrodynamic units:
\begin{equation}
\begin{matrix}
i\: \text{biot} = i\: (\sqrt{2}\: \text{ed}) = \sqrt{2}i\: \text{ed} = j\: \text{ed}\\
\text{where biot} = \sqrt{2}\: \text{ed and}\: \sqrt{2}\: i = j
\tag{c}
\end{matrix}
\end{equation}
Also:
\begin{equation}
\begin{matrix}
\phi\: \text{biot} = \phi\: (\sqrt{2}\: \text{ed}) = \sqrt{2}\phi\: \text{ed} = \Phi_j\: \text{ed}\\
\text{where biot} = \sqrt{2}\: \text{ed and}\: \sqrt{2}\: \phi = \Phi_j
\tag{d}
\end{matrix}
\end{equation}

Therefore in electrodynamic (by comparing with equation (1)):

$j$ (ed) = $\Phi_j$ (ed)

(c) While converting to electrostatic units:

\begin{equation}
\begin{matrix}
i\: \text{biot} = i\: (3\times10^{10}\: \text{StatAmp}) = 3\times10^{10}i\: \text{StatAmp} = k\: \text{StatAmp}\\
\text{where biot} = 3\times10^{10}\: \text{StatAmp and}\: 3\times10^{10}\: i = k
\tag{e}
\end{matrix}
\end{equation}

\begin{equation}
\begin{matrix}
\phi\: \text{biot} = \phi\: (3\times10^{10}\: \text{StatAmp}) = 3\times10^{10}\phi\: \text{StatAmp} = \Phi_k\: \text{StatAmp}\\
\text{where biot} = 3\times10^{10}\: \text{StatAmp and}\: 3\times10^{10}\: \phi = \Phi_k
\tag{f}
\end{matrix}
\end{equation}

Therefore in electrostatic units (by comparing with equation (1)):

$k$ (StatAmp) = $\Phi_k$ (StatAmp)

i.e. in all units, strength of the shell and strength of current flowing through its boundary are same.

Question 1: Am I correct?

if yes

Question 2: Then why is it said that "strength of the shell and strength of current flowing through its boundary are same only in certain units like electromagnetic units"?