On (pentagon shaped) electric field question.

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SUMMARY

The discussion focuses on calculating the electric field at the center of a regular pentagon formed by four charged particles, each with charge q, positioned at corners A, B, C, and D. The relevant equation for the electric field is E=q/(4∏ε0)(a^2). The participants emphasize the importance of vector resolution and symmetry in determining the net electric field, concluding that the electric fields from the charges at the corners must be decomposed into components for accurate summation. The net electric field at the center is zero due to the symmetrical arrangement of the charges.

PREREQUISITES
  • Understanding of electric fields and Coulomb's law
  • Familiarity with vector decomposition and addition
  • Knowledge of symmetry in physics
  • Basic grasp of electrostatics and charge interactions
NEXT STEPS
  • Study vector decomposition techniques in physics
  • Learn about electric field calculations for different charge configurations
  • Explore the concept of symmetry in electric fields
  • Investigate advanced electrostatics concepts, such as superposition principle
USEFUL FOR

Students studying electrostatics, physics educators, and anyone interested in understanding electric fields in symmetrical charge arrangements.

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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.
 
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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
 
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.
 

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