Is the scalar magnetic Potential the sum of #V_{in}# and ##V_{out}##

[happyparticle]

Hi,
I'm wondering if I have an expression for the scalar magnetic potential (V_in) and (V_out) inside and outside a magnetic cylinder and the potential is continue everywhere, which mean $V^1 - V^2 = 0$ at the boundary. Does it means that $V^1 - V^2 = V_{in} - V_{out} = 0$ ?

 

[Charles Link]

With these boundary conditions, it is understood that the potential(s) or field(s) are to be evaluated at some point on the boundary. e.g. when writing $V_{in} = V_{out}$, they often leave out at $r=a$, etc., but that is implied.

It is the case with both electrostatic and magnetic (fictitious) surface charges on the boundary, that the potentials are continuous across the surface charge , even though the perpendicular components of the $E$ or $H$ fields are not continuous, but are affected by the surface charge. So long as $E$ or $H$ remain finite, the potentials will be continuous across the surface charge distribution.