Find electric field on a point due to a charged arc.

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SUMMARY

The discussion focuses on calculating the electric field at the center of a circular arc with a uniform charge distribution of 25nC over a 90-degree angle and a radius of 2.0 m. The relevant formula used is E = k*Q/r^2, where k is Coulomb's constant. Participants clarify that the limits of integration for the electric field calculation should be set from -π/4 to π/4, and suggest using symmetry to simplify the algebra involved in the solution.

PREREQUISITES
  • Understanding of electric field concepts and Coulomb's law
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of charge distribution and arc length calculations
  • Basic understanding of symmetry in physics problems
NEXT STEPS
  • Review the derivation of electric field equations for continuous charge distributions
  • Practice integration techniques involving trigonometric functions
  • Explore the application of symmetry in electrostatics problems
  • Learn about the implications of charge distribution on electric fields
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those working on problems involving electric fields from charged arcs or segments.

cgar666
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Homework Statement


A charge of 25nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies?

I'm not getting the right answer however, so if someone would be able to help me solve this question and point out what I'm doing wrong I"d be very appreciative.

Homework Equations


E = k*Q/r^2
θ=s/r
dq = λ ds

The Attempt at a Solution


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The limits of integration should be \frac{-\pi}{4} to \frac{\pi}{4}.

The arc length is \frac{(2)(\pi)(r)}{4}.
 
The limits of integration should be \frac{-\pi}{4} to \frac{\pi}{4}.

No, cgar666 limits of integration are perfectly fine. They may just lead to more math. You can use symmetry to slightly clean up some algebra as well.
 

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