Point charges in a regular hexagon

[rbh]

Homework Statement

Regular hexagon with side length a, has q,q,q,q,-q,-q point charges in vertices. What force would point charge q expierence if it was put in a hexagon center?

Relevant Equations

F=(kq^2)/R^2
R=(sqrt3 × a)/2

The answer should be (2×sqrt3×k×q^2)/a^2. What did I do wrong?

 

[Steve4Physics]

I can't follow your working but...

Is 'a' the hexagon's side-length? Is 'R' the distance from an outer charge to the centre? If so, 'R=(sqrt3 × a)/2' is wrong!

Also, have you thought about the x and y components of each of the 6 forces on the centre charge? Then, using symmetry, the solution becomes very simple.

Edit - typo' corrected.

 

[rbh]

I can't follow your working but...

Is 'a' the hexagon's side-length? Is 'R' the distance from an outer charge to the centre? If so, 'R=(sqrt3 × a)/2' is wrong!

Also, have you thought about the x and y components of each of the 6 forces on the centre charge? Then, using symmetry, the solution becomes very simple.

Edit - typo' corrected.

Oh yeah, I mixed it up with inscribed circle radius, thanks.