Does This Answer Make Sense (basic EM)

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SUMMARY

The discussion centers on calculating the electric potential and electric field due to a non-uniform charge density on a plastic rod of length L=1 m, with charge density defined as λ=cx, where c=2x10-6. The electric potential V was calculated as V=17980V using the equation V=k*integral(cdx). However, there is contention regarding the limits of integration used by the teacher, which were taken from L to L+1, while the textbook specifies limits from 0 to L. This discrepancy raises questions about the correctness of the integration method applied.

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  • Understanding of electric potential and electric field concepts
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of charge density and its implications in electrostatics
  • Proficiency in using the equation V=k*integral(cdx)
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  • Review the derivation of electric potential from charge distributions
  • Learn about the implications of non-uniform charge density in electrostatics
  • Study the application of limits in definite integrals in physics problems
  • Explore the relationship between electric potential and electric field
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Students studying electromagnetism, physics educators clarifying concepts of electric potential, and anyone involved in solving electrostatic problems with non-uniform charge distributions.

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Homework Statement



The plastic rod of the length L=1 m has a non-uniform charge density λ=cx
where positive constant c =2x10-6 [some unit]. What unit does c have? Find the electric
potential at the point on the x-axis 1 m to the left from the left end of the rod. Find the
electric field at that point as well, preferably via potential.

Homework Equations



V=k*integral(cdx)

The Attempt at a Solution




V=kc*integral(dx)-----V=kcx------V=17980V

Is it just me or is this completely wrong? This is not my solution--it's my teacher and I was under the impression that the integral would end up being (with d=end of rod to point P):

V=kc*integral(x/d+x)-----V=kc[L-d(ln)(1+L/d)]

He ttok his limits of integration as L to L+1, however, in the book it says it should be from 0 to L (even though that doesn't really affect the answer). It is his integration I do not agree with.

Thanks in advance for any clarification.
 
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