Question

Compare the concepts of scalar and vector magnetic potentials.

Answer 1

The electric field can be represented by a scalar potential because in the absence of a changing magnetic field the curl of E equals zero (Faraday’s Law):
[math]\nabla \times \vec{E}=0[/math].
The curl of a gradient is always zero so that means that the electric field can be represented as the gradient of some function but that function has to be a scalar because gradients act on scalars. This is what is called the scalar potential [math]\phi[/math]:
[math]\vec{E}=-\nabla \phi[/math].
(The negative is just convention.)
Gauss’s Law for Magnetism says that there are no magnetic monopoles, or more mathematically speaking, the magnetic field doesn't diverge:
[math]\nabla \cdot \vec{B}=0[/math].
The divergence of a curl is always zero so the magnetic field is the curl of something. This something is the vector potential
[math]\vec{A}[/math] and it has to be a vector because you take the curl of vectors and not scalars.
[math]\vec{B}=\nabla \times \vec{A}[/math]
In special relativity the scalar and vector potentials are combined into what is called a 4-vector (vector with four components and not the usual three). This particular four vector is called the four potential and is denoted
[math]A^μ=\big( \phi /c[/math]
[math], A_x , A_y , A_z\big) =\big( \phi /c, \vec{A} \big)[/math]
,
where [math]μ[/math] is not an exponent but is an index that runs from 0–3 representing which component of the 4-vector you are talking about.

Hope this helped!

Answer 2

Hi mate

Here is ur answer ⬇⬇

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Magnetic scalar potential, ψ, is a quantity in classical electromagnetism analogous to electric potential. It is used to specify the magnetic H-field in cases when there are no free currents, in a manner analogous to using the electric potential to determine the electric field in electrostatics.