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

In summary, the net force on a test charge, Q, situated at the centre of a regular tridecagon with 13 equal charges at its corners will be zero due to the lack of symmetry. Even in regular polygons with an odd number of charges, the field at the centre is not zero as the contributions cannot cancel in pairs. Therefore, the structure of the argument needs to be carefully considered.
  • #1
lufbra08
5
0

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.
 
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  • #2
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.
 
Last edited:
  • #3
No. There is no centre of symmetry.

ehild
 

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

1. What is electric charge?

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. It can be either positive or negative, and is measured in units of Coulombs (C).

2. How is electric charge created?

Electric charge is created by the movement of electrons. When electrons move from one object to another, the object that gains electrons becomes negatively charged, while the object that loses electrons becomes positively charged.

3. What is the net force on a charged object?

The net force on a charged object is the sum of all the individual forces acting on it due to other charged objects. This can be calculated using Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

4. How is electric charge distributed on an object?

Electric charge is distributed on an object either uniformly or non-uniformly, depending on the material and its shape. In a conductor, the charge is distributed evenly on the surface, while in an insulator, the charge tends to accumulate at specific points on the surface.

5. What is the difference between electric force and electric field?

Electric force is the force that one charged object exerts on another, while electric field is the region around a charged object where another charged object experiences a force. Electric field is a vector quantity, while electric force is a scalar quantity.

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