Deriving electric and vector potential

[DirecSa]

Homework Statement:

To give the Maxwell equations and material equations of electrostatics relevant to infinitely extensive area and deriving the electric potential and vector potential.

Relevant Equations:

Maxwell equations.

1- Write down the complete MAXWELL equations in differential form and the material equations.

2- An infinitely extensive area is homogeneously filled with a material with a location-dependent permittivity. There are charges in the area. Give the Maxwell equations and material equations of electrostatics relevant for this area and derive the equation for the scalar electrical potential ϕ from them using a suitable approach (Ansatz, justification)..

3- An infinitely extensive area is filled with a material with location-dependent permeability. There are currents of known current density in the area. State the MAXWELL equations and material equations of magneto-statics relevant for this area and derive the equation for the magnetic vector potential A⃗⃗ using a suitable approach (Ansatz, justification).

Above it is one question and have three parts. Part 2 and part 3 of the question I can't understand, what it wants exactly... what is the difference from part 1... rather than writing potential equation or the vector potential. I have no clue what to do or how to start, please what exactly they want from me and what Ansatz they ask for :|

 

[rc1]

Assuming I understand the question correctly... though I might be completely wrong here... interesting question.

Permitivity relates to electric fields . Permaebility relates to magnetic fields.

Usually- Electrostatics considers point charges- Magnetostatics considers linear currents in an infinite wire.

In this case the charge and magnetism is a function of location- ie- Permitivity is a function of (radius, angle, angle) and permeability is a function of (radius, angle, angle).

Just plug the above permitivity and permaebility into Maxwell's equations and ...

2. derive the equation for the scalar electrical potential ϕ

3. derive the equation for the magnetic vector potential A⃗⃗

 

[rude man]

For (3) your textbook should do it for you.
It involves a bit of fancy vector calculus and some comparison with the derivation of the electrostatic scalar potential.