# Deriving electric and vector potential

• DirecSa
In summary: You are essentially trying to solve for A⃗⃗ using the vector form of Maxwell's equations and then comparing it to the scalar potential solution for electrostatics.In summary, the conversation discusses the derivation of Maxwell equations and material equations for an infinitely extensive area filled with a material with location-dependent permittivity and permeability. The main focus is on deriving the equations for the scalar electrical potential and the magnetic vector potential using a suitable approach, such as an Ansatz and justification. This involves plugging the location-dependent permitivity and permeability into the Maxwell equations and using some vector calculus techniques to solve for the potentials.
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 :|

Last edited:
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

berkeman
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.

## 1. What is the purpose of deriving electric and vector potential?

The purpose of deriving electric and vector potential is to understand the behavior of electric fields and how they interact with charged particles. This allows scientists to make predictions and calculations about the movement and distribution of charges in a given system.

## 2. How is electric potential different from electric field?

Electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space, while electric field is a vector quantity that represents the force per unit charge at a given point in space. In other words, electric potential describes the energy of a charge in an electric field, while electric field describes the force on a charge in an electric field.

## 3. What is the relationship between electric potential and electric field?

The relationship between electric potential and electric field is described by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator. This means that the electric field is equal to the negative gradient of the electric potential.

## 4. How is vector potential related to magnetic fields?

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

## 5. What are some real-world applications of deriving electric and vector potential?

Some real-world applications of deriving electric and vector potential include designing and analyzing electrical circuits, understanding the behavior of charged particles in particle accelerators, and studying the movement of charged particles in space. It is also used in the development of technologies such as MRI machines and electric motors.

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