On (pentagon shaped) electric field question.

[physikamateur]

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.

 

[physikamateur]

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

 

[tms]

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.