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

  • #1
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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  • #2
Charles Link
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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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