On (pentagon shaped) electric field question.

AI Thread Summary
The discussion revolves around calculating the electric field at the center of a regular pentagon with charges placed at its corners. The electric field equation E=q/(4∏ε0)(a^2) is mentioned, but the contributor suggests that simply summing the fields from the four corners is insufficient due to the pentagon's symmetry. They propose that the electric fields from the charges must be resolved into components to accurately determine the net electric field. The importance of symmetry in simplifying the calculations is emphasized, and the contributor refers to a diagram hosted on their blog for clarity. Ultimately, understanding vector decomposition is crucial for solving the problem effectively.
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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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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
 
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.
 

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