What is the net force on a test charge at the centre of a tridecagon?

[lufbra08]

Homework Statement

13 equal charges, q, are situated at the corners of a regular tridecagon. What is the net force on a test charge, Q, situated at the centre.

Homework Equations

F=k(qQ/r^2) r^

(r^=r vector/r)

The Attempt at a Solution

The net force will be zero due to the symetry of the tridecagon.

 

[kuruman]

What symmetry? Symmetry arguments work in regular polygons when you have an even number of vertices and therefore an even number of charges. Then the electric field at the centre is zero because contributions from charges cancel in pairs. Here you have an odd number of charges. They cannot cancel in pairs. Is the field at the centre still zero, though? You need to structure your argument more carefully.

 

[ehild]

No. There is no centre of symmetry.

ehild