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

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SUMMARY

The net force on a test charge, Q, located at the center of a regular tridecagon with 13 equal charges, q, positioned at its corners is not zero. Due to the odd number of charges, symmetry does not allow for the cancellation of forces in pairs, which is a characteristic of even-numbered polygons. The electric field at the center of the tridecagon does not achieve equilibrium, leading to a non-zero net force on the test charge.

PREREQUISITES
  • Understanding of electric force and Coulomb's law (F = k(qQ/r²))
  • Knowledge of symmetry in geometric shapes, particularly polygons
  • Familiarity with vector analysis in physics
  • Concept of electric fields and their behavior in multi-charge systems
NEXT STEPS
  • Study the implications of symmetry in electric fields for regular polygons
  • Explore the behavior of electric fields in systems with odd versus even charge distributions
  • Learn about vector addition of forces in electrostatics
  • Investigate the concept of electric potential in relation to charge configurations
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those interested in the effects of charge distributions on electric fields.

lufbra08
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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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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:
No. There is no centre of symmetry.

ehild
 

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