Non-Uniform Distribution of Charge on a Rod

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SUMMARY

The discussion focuses on calculating the potential due to a non-uniformly charged rod, where the charge density is defined as λ = ax, with a being a constant. The constant a is determined to be a = (2Q)/(L²). The potential V at a point along the positive x-axis is derived from the integral of the charge distribution, leading to the equation V = ∫(ax dx)/(4π)(ε₀)r. The user seeks clarification on the variable r, questioning whether it represents the distance x from the charge.

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  • Proficiency in using the equations for charge density and potential
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Homework Statement



A rod of length L lies along the x-axis with its left end at the origin. A total charge Q is distributed non-uniformly on the rod, so that ?=ax, where a is a positive constant. (a)Determine the constant a. (b) What is the potential due to this charged rod at a point along the positive x-axis, past the end of the rod? (c) A point charge +2Q is placed at 3L from the origin on the positive x-axis. What is the potential energy of this system?

Homework Equations


dq=λds
dV=(dq)/(4pi)(ε0)r
dU=Vdq

The Attempt at a Solution


I completed part a and got a=(2Q)/(l2)

my attempt at part b:
V=∫dV=∫(ax dx)/(4pi)(ε0)r

From there my question is more what is the value of r? is it x? From there I am sure i can figure out the rest.
 
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r is the distance from the charge. A picture would help.

ehild
 

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