# Magnetic Vector Potential Around a Wire Carrying Current

• snoopies622
In summary, the conversation discusses the concept of magnetic vector potential and its definition in relation to the magnetic field. The conversation also mentions the use of Fitzpatrick's equations and the gauge condition for the magnetic vector potential. Additionally, the Lagrangian of a charged particle in an electromagnetic field is brought up, with a reference to an equation for it.
snoopies622
Until about ten minutes ago I had never heard of the magnetic vector potential $$\vec A$$, defined such that

$$\vec B = \nabla \times \vec A$$.

I am having trouble visualizing this. What would the magnetic vector potential field look like around a straight wire carrying a (constant) electric current?

Thanks atyy, that's a great reference.

Is the Lagrangian of a charged particle in an electromagnetic field

$$L = \frac {1}{2}m( \dot x ^2 + \dot y^2 + \dot z^2 ) - q \phi + q (\dot x A_x + \dot y A_y + \dot z A_z) ?$$

(I'm not sure if that should be $$-q \phi$$ or $$+ q \phi$$.) If so, is this good for both static and changing EM fields?

Edit: oh wait, here it is. Equation 1.34. at

http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp1.pdf

All set, then.

Last edited:

## 1. What is the magnetic vector potential?

The magnetic vector potential is a fundamental quantity in electromagnetism that is used to describe the magnetic field around a current-carrying wire or other current-carrying objects. It is defined as the vector quantity whose curl equals the magnetic field.

## 2. How is the magnetic vector potential calculated around a wire carrying current?

The magnetic vector potential around a wire carrying current is given by the formula A = μ0I/4πr, where μ0 is the permeability of free space, I is the current in the wire, and r is the distance from the wire. This formula can also be derived using the Biot-Savart law.

## 3. What is the direction of the magnetic vector potential around a wire carrying current?

The magnetic vector potential around a wire carrying current is a vector quantity and its direction is perpendicular to both the current direction and the distance from the wire. This means that the direction of the magnetic vector potential forms a circular pattern around the wire.

## 4. How does the magnetic vector potential change as the distance from the wire increases?

The magnetic vector potential decreases as the distance from the wire increases. This is because the farther away from the wire, the weaker the magnetic field becomes and thus the lower the value of the magnetic vector potential.

## 5. Can the magnetic vector potential be measured directly?

No, the magnetic vector potential cannot be measured directly. It is a mathematical construct used to help describe the behavior of magnetic fields around current-carrying objects. However, its effects can be observed and measured indirectly through the magnetic field it produces.

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