Calculating Electric Potential for a Wire with Linear Charge Density?

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SUMMARY

The discussion focuses on calculating the electric potential at the center of a semicircular wire with a linear charge density, denoted as λ. The potential from the semicircle is given by the formula V = KQ/R, where K is the Coulomb's constant. To compute the potential from the two straight wire segments, the charge on a small element dx is expressed as λ*dx, and the potential contribution from this segment is calculated using dV = K*λ*dx/(R + x). The total potential from the two straight pieces is obtained by integrating this expression from x = R to x = (2R + R) and then doubling the result.

PREREQUISITES
  • Understanding of electric potential and charge density concepts
  • Familiarity with calculus, particularly integration techniques
  • Knowledge of Coulomb's law and constants, specifically Coulomb's constant (K)
  • Basic physics principles related to electric fields and potentials
NEXT STEPS
  • Study the derivation of electric potential from continuous charge distributions
  • Learn about integration techniques for calculating potentials in electrostatics
  • Explore the applications of Coulomb's law in various geometries
  • Investigate the concept of electric field and its relationship with electric potential
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Students studying electromagnetism, physics educators, and anyone interested in advanced electrostatics calculations.

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Homework Statement


the wire in the image below has a linear charge density \lambda . what is the electric potential at the center of the semicircle?
http://img18.imageshack.us/img18/5139/physicsproblem.jpg

Homework Equations


The Attempt at a Solution


i know that the potential from the semi circle is V=KQ/R
but I am having a little trouble figuring out how to calculate the potential from the other 2R pieces of wire.
can someone help me out here :)
 
Last edited by a moderator:
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Consider a small element dx at a distance x from the center P on either 2R piece. Charge on this piece is lambda*dx. Potential due to this piece dV = K*lambda*dx/( R + x ). To find the potential due one piece find the integration between the limits x = R to x = (2R + R). Then double it to get the total potential due to two straight pieces.
 
Last edited:
rl.bhat said:
Consider a small element dx at a distance x from the center P on either 2R piece. Charge on this piece is lambda*dx. Potential due to this piece dV = K*lambda*dx/( R + x ). To find the potential due one piece find the integration between the limits x = R to x = (2R + R). Then double it to get the total potential due to two straight pieces.

thanks allot for the help
 

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