Scalar Potentials and Electromagnetic Current

In summary, the conversation discusses finding the scalar potential, charge density, and electromagnetic current for a dipole and a solenoid. The equations -grad^2(phi) + 1/c^2*d/dt(phi) = rho/epsillon0 and -grad^2(A(phi/c,a)) + 1/c^2*d/dt(A(phi/c,a)) = mic0*J(rho*c,j) are used to derive these values. The conversation also mentions using the Biot-Savart law to find the magnetic field of a solenoid and the magnetic moment to calculate the magnetic field of the Earth and other planets. However, it is noted that the magnetic field around the Earth is more complex and not accurately
  • #1
Philosophaie
462
0
For a Dipole and a Torad (or a Solenoid) I need to find the scalar Potential,phi, Charge Density,rho, and then 4-Electromagnetic Current,J(rho*c,j) where A and J are 4-vectors and a and j are 3-vectors.

-grad^2(phi) + 1/c^2*d/dt(phi) = rho/epsillon0

where grad(A(phi/c,a)) = -1/c^2*d/dt(phi)

-grad^2(A(phi/c,a)) + 1/c^2*d/dt(A(phi/c,a)) = mic0*J(rho*c,j)

I need a little help deriving rho, phi and J for a copper solenoid of diameter, d.
This is not a homework problem this is for my personal use.
 
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  • #2
Is there any reason you want to solve everything in terms of Lorenz invariant equations? The 3-magnetic field of a dipole can be found by looking at the magnetic potenial ##\mathbf{A}## of a dipole and the field from a solenoid can be found using the Biot-Savart law.
 
  • #3
The magnetic fields of the Earth (Neglecting the Sun Fields, Solar Wind, etc.) can be calculated by using the magnetic moment. The magnetic moment is located on the z-axis relative to the x- plane of the equator. What is the magnitude of this magnetic moment so the others can be calculated? Also could this be calcated for the other planets and the sun (neglecting its periodic nature).
 
  • #4
Philosophaie said:
The magnetic fields of the Earth (Neglecting the Sun Fields, Solar Wind, etc.) can be calculated by using the magnetic moment. The magnetic moment is located on the z-axis relative to the x- plane of the equator. What is the magnitude of this magnetic moment so the others can be calculated? Also could this be calcated for the other planets and the sun (neglecting its periodic nature).
Not quite. The magnetic field around the Earth and other planets is rather complicated and does not match that of a simple dipole even when ignoring external influences. Here are some magnetic maps showing different elements of the Earth's magnetic field.
https://www.ngdc.noaa.gov/geomag/WMM/image.shtml
 
  • #5
The Gaussian model of Earth give a better approximation but is very difficult to formulate. Are there other mathematical models to give better approxs?
 

What is a scalar potential?

A scalar potential is a mathematical function that is used to describe the potential energy of a system in terms of a scalar quantity. In the context of electromagnetism, it is used to describe the electric potential energy of a charged particle in an electric field.

How is a scalar potential related to an electromagnetic field?

A scalar potential is related to an electromagnetic field through the concept of electric potential. The electric potential at a point in space is equal to the scalar potential multiplied by the charge at that point. This relationship is described by the equation V = φq, where V is the electric potential, φ is the scalar potential, and q is the charge.

What is the equation for the scalar potential?

The equation for the scalar potential is φ = ∫E•dl, where φ is the scalar potential, E is the electric field, and dl is an infinitesimal length element along the path of integration. This equation is based on the concept of conservative fields, where the work done by a conservative field is independent of the path taken.

What is electromagnetic current?

Electromagnetic current is a term used to describe the flow of electric charge through a conductor. It is generated by the movement of charged particles, such as electrons, and is an important factor in the behavior of electrical circuits and devices.

How are scalar potentials and electromagnetic current related?

Scalar potentials and electromagnetic current are related through the concept of electric potential. The electric potential at a point in a circuit is equal to the scalar potential multiplied by the current at that point. This relationship is described by the equation V = φI, where V is the electric potential, φ is the scalar potential, and I is the current.

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