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

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The discussion centers on the scalar magnetic potential (V_in and V_out) within and outside a magnetic cylinder, emphasizing that the potential must be continuous at the boundary, leading to the equation V^1 - V^2 = 0. This implies that V_in equals V_out at the boundary, typically evaluated at a specific point like r=a. The conversation draws parallels to electrostatics, noting that while the potentials remain continuous across surface charges, the perpendicular components of the electric (E) or magnetic (H) fields may not be. The continuity of potentials is maintained as long as the fields remain finite, despite the influence of surface charges. Overall, the discussion highlights the importance of boundary conditions in determining the behavior of scalar magnetic potentials.
happyparticle
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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## ?
 
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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.
 
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