On (pentagon shaped) electric field question.

In summary, the problem involves four particles with equal charge placed on the corners of a regular pentagon, with the distance from each corner to the center being a. The goal is to find the electric field at the center of the pentagon, which can be calculated using the equation E=q/(4∏ε0)(a^2). The method for determining the net electric field involves adding the individual electric fields of each particle, taking into account their direction and symmetry.
  • #1
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Homework Statement


Four particles, each having a charge q are placed on the four corners A, B, C, D of a regular pentagon ABCDE. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.


Homework Equations


E=q/(4∏ε0)(a^2) where k=1/4∏ε0

The Attempt at a Solution


Well certainly I think it's silly to just sum up four electric fields to give 4q/(4∏ε0)(a^2). I think it would seem obvious that there is a net electric field as shown in the attached diagram. Suppose E(E) exists. Then E(A)+E(B)+E(C)+E(D)+E(E)=0. My working is shown in the diagram attached. At the same time I am confused as how the electric field vectors resolves.
 
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  • #2
Darn, can't upload the diagrams. I've uploaded it on my random blog. Go to www.kcsuploads.blogspot.com and see pentagon diagram. Sorry for any inconvenience caused
 
  • #3
Just add the vectors the way vectors add. Decompose them into their components in a convenient reference frame. Symmetry considerations will help set that up.
 

1. What is a pentagon-shaped electric field?

A pentagon-shaped electric field is an electric field that has five sides in the shape of a pentagon. It is created by electric charges that are arranged in a pentagon shape.

2. How is a pentagon-shaped electric field different from other electric fields?

Pentagon-shaped electric fields are unique because they have a more complex shape compared to other electric fields, which are typically created by point charges or parallel plates. They can also have different strengths and directions at different points in the field due to the asymmetry of the shape.

3. What causes a pentagon-shaped electric field?

A pentagon-shaped electric field is caused by the distribution of electric charges in a pentagon shape. This can occur naturally, such as in the case of a pentagon-shaped crystal, or it can be artificially created by placing charged objects in a pentagon pattern.

4. How is the strength of a pentagon-shaped electric field measured?

The strength of a pentagon-shaped electric field can be measured using a device called an electric field meter. This device measures the force exerted on a charged particle placed in the field and can give a quantitative measurement of the field's strength at a specific point.

5. What are some real-life applications of pentagon-shaped electric fields?

Pentagon-shaped electric fields are used in a variety of scientific and technological applications. They are commonly used in particle accelerators to manipulate and control the paths of charged particles. They are also used in advanced imaging techniques, such as electron microscopy, and in the study of crystal structures. Additionally, they have potential applications in the development of new electronic devices and materials.

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