Vector potential of a plate with a uniform, time-harmonic current density

In summary, the conversation revolved around finding an expression for A2 vector potential and the assumptions needed to derive it. The speaker also mentioned the usefulness of approximations in engineering for practical antenna systems.
  • #1
Veronika
1
0
Hi all,

i tried to do this question but got stuck on the last point . Can anyone help me please?
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The general form of vector potential:
upload_2018-4-9_12-42-29.png


I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it?

Thank you , Veronika
 

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  • #2
I believe what they are asking you to do is first find an expression for A2 using the same approximations as you used for A1, then determine under what conditions your expression is well approximated by their expression.

By the way, these kinds of approximations are incredibly useful and engineers use them all of the time when analyzing practical antenna systems.
 

1. What is the vector potential of a plate with uniform current density?

The vector potential of a plate with uniform current density is a mathematical concept used to describe the magnetic field generated by a constant and evenly distributed flow of electric current on a flat surface. It is a vector quantity that represents the directional and magnitude information of the magnetic field.

2. How is the vector potential of a plate with uniform current density calculated?

The vector potential of a plate with uniform current density can be calculated using the formula A = μ0I/2π * ln(r/r'), where A is the vector potential, μ0 is the permeability of free space, I is the current density, r is the distance from the center of the plate, and r' is the distance from a reference point outside the plate.

3. What is the significance of the time-harmonic current density in the vector potential of a plate?

The time-harmonic current density in the vector potential of a plate refers to a current that varies sinusoidally with time. This type of current is commonly used in electrical systems, and by incorporating it into the vector potential formula, we can analyze the behavior of the magnetic field over time.

4. How does the shape and size of the plate affect the vector potential?

The shape and size of the plate can greatly affect the vector potential. For example, a larger plate will have a stronger magnetic field and a more spread-out vector potential, while a smaller plate will have a weaker field and a more concentrated vector potential. The shape of the plate can also impact the direction and distribution of the vector potential.

5. What are some practical applications of understanding the vector potential of a plate with uniform current density?

Understanding the vector potential of a plate with uniform current density has many practical applications, including in the design and analysis of electromagnetic devices such as motors, generators, and transformers. It is also used in the study of electromagnetic fields and can aid in the development of new technologies in areas such as power generation and transportation.

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