Magnetic vector potential

In summary, the magnetic vector potential is a mathematical concept used in electromagnetism to describe the magnetic field in a given region. It is related to the magnetic field through the equation B = ∇ x A, where B is the magnetic field and A is the magnetic vector potential. Some applications of the magnetic vector potential include in the design of magnetic devices, the study of electromagnetic radiation, and the calculation of magnetic forces on moving charged particles. It is different from the electric potential in that it is a vector quantity and is only defined in regions with non-zero electric current. The magnetic vector potential cannot be measured directly, but is a useful tool in solving problems in electromagnetism.
  • #1
pardesi
339
0
Why is the magnetic vector potential of a point inside a infinite soleniod azimuthal assuming the axis of solenoid is the z axis.
Problem is the formulae [itex]A(\vec r)=\int_{v} \frac {\vec J(\vec r^{'})}{r} d\tau [/itex] doesn't hold any more due to the infinite extent of the current
 
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  • #2
When you say "why is" I assume you mean "what is", and A is simple to find in this case because you can find B using the integral form of ampere's law and then guess A by looking at B = Curl(A).
 
  • #3
distribution

The magnetic vector potential is a fundamental concept in electromagnetism that is used to describe the magnetic field in a given region of space. It is a vector field that is defined in terms of the current density in the region and is used to calculate the magnetic field at any point.

In the case of an infinite solenoid, the magnetic vector potential is assumed to be azimuthal, meaning it is oriented along the axis of the solenoid, which is typically taken to be the z axis. This is because the solenoid is assumed to have an infinite extent, meaning it extends infinitely in the z direction. As a result, the magnetic field is also expected to be azimuthal, with no variation in the z direction.

However, the formula A(\vec r)=\int_{v} \frac {\vec J(\vec r^{'})}{r} d\tau does not hold for an infinite solenoid because of the infinite extent of the current distribution. This formula is based on the assumption of a finite current distribution, where the current density is confined to a specific volume. In the case of an infinite solenoid, the current density is spread out infinitely along the z axis, making it impossible to integrate over a finite volume.

To properly describe the magnetic vector potential in an infinite solenoid, a different approach is needed. One possible solution is to use a different coordinate system, such as cylindrical coordinates, where the z axis is the axis of the solenoid. This allows for a more appropriate representation of the infinite current distribution and the resulting magnetic field.

In conclusion, the magnetic vector potential is an important concept in electromagnetism that is used to describe the magnetic field in a given region of space. In the case of an infinite solenoid, the assumption of an azimuthal magnetic vector potential is made due to the infinite extent of the current distribution along the z axis. However, this assumption also requires a different approach to calculating the magnetic vector potential, as the standard formula does not hold for an infinite current distribution.
 

What is the magnetic vector potential?

The magnetic vector potential is a mathematical concept used in electromagnetism to describe the magnetic field in a given region. It is a vector quantity that is determined by the electric current flowing in a region and can be calculated using the Biot-Savart law.

How is the magnetic vector potential related to the magnetic field?

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

What are some applications of the magnetic vector potential?

The magnetic vector potential has many applications in electromagnetism, including in the design of magnetic devices such as motors and generators. It is also used in the study of electromagnetic radiation and in the calculation of magnetic forces on moving charged particles.

How is the magnetic vector potential different from the electric potential?

The magnetic vector potential is a vector quantity, while the electric potential is a scalar quantity. Additionally, the magnetic vector potential is only defined for regions where there is a non-zero electric current, while the electric potential can exist in regions with no current. However, both concepts are important in understanding and describing electromagnetic phenomena.

Can the magnetic vector potential be measured directly?

No, the magnetic vector potential cannot be measured directly. It is a mathematical construct used to describe the magnetic field and cannot be measured with physical instruments. However, it is a useful concept in solving problems in electromagnetism and can be calculated using mathematical equations.

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