Electric Potential Homework: Circle of Radius 5 cm

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SUMMARY

The electric potential at the center of a circle with a radius of 5 cm, formed by a wire with a charge density of λ = 0.1 C/m, is calculated using the formula V = Q/(4πε₀r). The total charge Q can be determined by Q = 2πrλ, leading to the conclusion that the radius does not affect the potential at the center due to the symmetry of the charge distribution. The integration of the electric field from the center to infinity is an alternative method to derive the same result.

PREREQUISITES
  • Understanding of electric potential and charge density
  • Familiarity with the formula V = Q/(4πε₀r)
  • Knowledge of integration techniques in physics
  • Basic concepts of electric fields and their calculations
NEXT STEPS
  • Study the derivation of electric potential from charge distributions
  • Learn about the application of Gauss's Law in electrostatics
  • Explore the concept of electric fields generated by continuous charge distributions
  • Investigate the integration of electric fields to find potential differences
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Students studying electromagnetism, physics educators, and anyone interested in understanding electric potential and charge distributions in circular geometries.

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Homework Statement


A wire carrying a charge density of λ=.1c/m is bent into a circle of radius r = 5 cm. What is the electric potential at the center of the circle

Homework Equations

The Attempt at a Solution


λ/2Ԑ0 is this right? i do not really understand it or where my radius went
 
Last edited:
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It does appear the potential is ## V=Q/(4*\pi*\epsilon_o*r) ## and ## Q=2*\pi*r*\lambda ## A more lengthy approach to compute V would be to integrate the electric field from the center to infinity. Anyway, I think you can see how the "r" dropped out. Your answer is correct. The potential from a distribution of charges is the sum of all the potentials from infinitesimal elements of these charges.
 

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