Vector potential square loop

In summary, the conversation discusses calculating the vector potential and magnetic induction for a current flowing in a thin wire bent around a square. The problem is solved by breaking up the integral into four components, one for each side of the square, and then computing and adding them together. However, the answer obtained was incorrect and the person is asking for assistance.
  • #1
shehab
5
0

Homework Statement



A current I flows counter-clockwise in a thin wire bent around a square form of side 2a. Calculate the vector potential A and the magnetic induction B along an axis passing through the center of the square parallel to one of the sides. for definiteness, assume the loop lies in the x-y plane and choose the axis parallel to the x-side, so make your calculation for the point (x,a,0).

Homework Equations



A = (u0 I/4pi) x integral(dl/r)

The Attempt at a Solution

 
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  • #2
I attempted to solve this problem by breaking up the integral into four components, one for each side of the square. I then computed the integral for each side and added them together, but the answer I got was incorrect. Any help would be appreciated.
 

1. What is a vector potential square loop?

A vector potential square loop is a type of electromagnetic field that is created by a square-shaped loop of wire. It is a representation of the magnetic field generated by a steady current flowing through the loop.

2. How is the vector potential square loop calculated?

The vector potential square loop is calculated using the Biot-Savart law, which states that the magnetic field at a given point is proportional to the current flowing through the loop and the distance between the point and the loop.

3. What are the applications of vector potential square loop?

The vector potential square loop has several applications in electromagnetics, including in the design of electric motors, generators, and transformers. It is also used in magnetic field sensors and in the analysis of magnetic materials.

4. What is the difference between vector potential square loop and magnetic field?

The vector potential square loop is a mathematical representation of the magnetic field, while the magnetic field is a physical quantity that describes the strength and direction of the magnetic force at a given point. The vector potential square loop is used to calculate the magnetic field at a specific point.

5. Are there any limitations to using vector potential square loop?

While vector potential square loop is a useful tool in electromagnetics, it is not always applicable in real-world situations. It assumes that the current is steady and does not take into account any changing magnetic fields or other complexities that may occur in practical applications.

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