Calculating Electric Potential for a Wire with Linear Charge Density?

AI Thread Summary
The discussion focuses on calculating the electric potential at the center of a semicircular wire with a linear charge density, λ. The potential from the semicircle is given by the formula V = KQ/R, but the challenge lies in determining the potential from the two straight wire segments. To address this, a small element dx is considered, where the charge on this segment is λ*dx, and the potential contribution is calculated as dV = K*λ*dx/(R + x). Integration is suggested between the limits x = R to x = (2R + R) to find the total potential from one straight piece, which is then doubled for both segments. The discussion concludes with an expression of gratitude for the assistance received.
mjolnir80
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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 :)
 
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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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