Vector magnetic potential of current sheet

In summary, the formula for the vector magnetic potential in the context of an infinite sheet of current is given by \mathbf A=\frac{\mu_0}{4\pi}\int_{V'}\frac{\mathbf J}{R}dv'. However, the integral does not converge. To solve this issue, \nabla\times\mathbf A can be calculated by moving the \nabla\times inside the integral. It is impossible to calculate \mathbf A for an infinite current sheet as its potential does not converge at infinity, but a local potential can be defined. The same issue arises when calculating the potential V of an infinite sheet of charge, but the electric field \mathbf E can be calculated
  • #1
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Hi. Say I have an infinite sheet of current. My book gives the following formula for the vector magnetic potential

[tex]
\mathbf A=\frac{\mu_0}{4\pi}\int_{V'}\frac{\mathbf J}{R}dv'
[/tex]

But when I do the integral, it doesn't converge. However, if I calculate [itex]\nabla\times\mathbf A[/itex], i.e. move the [itex]\nabla\times[/itex] inside the integral, it works out fine. Is it really impossible to calculate [itex]\mathbf A[/itex] for an infinite current sheet? I have the same problem if I try to calculate the potential [itex]V[/itex] of an infinite sheet of charge, but for the electric field [itex]\mathbf E[/itex] it works out fine.
 
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  • #2
No. The potential of an infinite sheet does not converge at infinity. But you can define a local potential.
 

1. What is the vector magnetic potential of a current sheet?

The vector magnetic potential of a current sheet is a mathematical representation of the magnetic field produced by a thin, flat sheet of electric current. It is a vector quantity that describes the strength and direction of the magnetic field at any given point in space.

2. How is the vector magnetic potential of a current sheet calculated?

The vector magnetic potential of a current sheet can be calculated using the Biot-Savart law, which states that the magnetic field produced by a small segment of current is directly proportional to the current and inversely proportional to the distance from the current segment.

3. What is the significance of the vector magnetic potential of a current sheet?

The vector magnetic potential of a current sheet is important in the study of electromagnetic fields and their effects on materials and objects. It is also used in the design and analysis of devices such as motors, generators, and transformers.

4. How does the vector magnetic potential of a current sheet relate to the magnetic vector potential?

The magnetic vector potential is a generalization of the vector magnetic potential and is used to describe the magnetic field in more complex situations. The vector magnetic potential of a current sheet can be derived from the magnetic vector potential by taking the curl.

5. Can the vector magnetic potential of a current sheet be measured experimentally?

No, the vector magnetic potential of a current sheet is a mathematical construct and cannot be directly measured. However, the magnetic field produced by a current sheet can be measured and used to calculate the vector magnetic potential.

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