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

In summary, the conversation discusses the continuity of the scalar magnetic potential (V_in) and (V_out) inside and outside a magnetic cylinder. The potential is continuous everywhere, meaning that V^1 - V^2 = 0 at the boundary. This also implies that V^1 - V^2 = V_{in} - V_{out} = 0. It is also mentioned that the potentials are evaluated at some point on the boundary, such as r=a. Additionally, the conversation touches on the continuity of the potentials across surface charges, even though the perpendicular components of the E or H fields may not be continuous. As long as E or H remain finite, the potentials will be continuous across the surface charge distribution.
  • #1
happyparticle
405
20
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
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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Related to Is the scalar magnetic Potential the sum of #V_{in}# and ##V_{out}##

1. What is scalar magnetic potential?

Scalar magnetic potential is a concept in physics that refers to the potential energy of a magnetic field at a given point in space. It is a scalar quantity, meaning it has magnitude but no direction.

2. What is #V_{in}# and ##V_{out}##?

#V_{in}# and ##V_{out}## are symbols used to represent the magnetic potential energy of the magnetic field inside and outside of a given region, respectively. They are often used in equations to calculate the total scalar magnetic potential.

3. Is the scalar magnetic potential the same as magnetic field?

No, the scalar magnetic potential and magnetic field are two different concepts. While magnetic field refers to the physical force exerted by a magnetic field on a charged particle, scalar magnetic potential refers to the potential energy of the magnetic field at a given point in space.

4. How is the scalar magnetic potential calculated?

The scalar magnetic potential is calculated by taking the sum of the magnetic potential energy inside and outside of a given region. This can be represented mathematically as #V_{in}# + ##V_{out}##.

5. What is the significance of the scalar magnetic potential?

The scalar magnetic potential is an important concept in physics as it helps us understand the behavior of magnetic fields and their effects on charged particles. It is also used in various calculations and equations in electromagnetism and other fields of physics.

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