Can the B field be obtained from the magnetic potential using matrix inversion?

In summary, the conversation discusses the relationship between the magnetic potential and field, with the main question being how to obtain the B field from the magnetic potential. The suggestion of converting the curl into matrix format is mentioned, but it is noted that the corresponding matrix cannot be inverted. It is then clarified that the correct question is how to obtain the A field from the B field, with the recommended solution being to consult an E&M book for discussion on Green's functions. The conversation ends with a potential formula for calculating the A field and a thank you to Dr. T for the help.
  • #1
sinyud
23
0
How do you get the B field from the magnetic potential?
I tried converting the curl into matrix format, but the corresponding matrix can't be inverted.
 
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  • #2
It's just the curl of the vector potential:

[tex]\vec B = \nabla \times \vec A[/tex]

I'm not sure what you're tyring to do with it.
 
  • #3
I got it backward. How do you the A field from a B field?
 
  • #4
Oh! Well in that case ... it depends on what problem you're trying to solve. Check with a good E&M book for some discussion on Green's functions. That might help. It's been a while since I worked with that so I'd have to review it myself.
 
  • #5
[tex] \vec{A} = \pm \frac{1}{2} \vec{B} \times \vec{r} [/tex] if memory serves me correctly...
 
  • #6
Thanks, Dr. T! Sinyud could easily check that by calculating the curl.
 

1. What is magnetic vector potential?

The magnetic vector potential is a mathematical concept used in electromagnetism to describe the magnetic field in terms of a vector quantity. It is defined as the vector field whose curl is equal to the magnetic field.

2. How is magnetic vector potential related to magnetic field?

The magnetic vector potential is related to the magnetic field through the equation B = ∇ x A, where B is the magnetic field, A is the magnetic vector potential, and ∇ x is the curl operator. This means that the magnetic field can be derived from the magnetic vector potential.

3. What is the significance of magnetic vector potential?

Magnetic vector potential is significant because it simplifies the mathematical description of magnetic fields and allows for easier calculations. It is also used in many practical applications, such as in the design of magnetic devices and in the study of electromagnetic waves.

4. How is magnetic vector potential different from electric potential?

Magnetic vector potential and electric potential are both vector fields, but they have different physical meanings. While magnetic vector potential is used to describe the magnetic field, electric potential is used to describe the electric field. Additionally, electric potential is a scalar quantity while magnetic vector potential is a vector quantity.

5. How can magnetic vector potential be calculated?

Magnetic vector potential can be calculated using the Biot-Savart law, which relates the magnetic field at a point to the current flowing through a wire. It can also be calculated using the vector potential equation, which involves solving a differential equation known as the Poisson equation.

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