Force on a point charge near a uniformly charged rod

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SUMMARY

The discussion focuses on the correct setup of the integral for calculating the force on a point charge near a uniformly charged rod. It emphasizes the importance of distinguishing between the constant length of the rod (denoted as ##l##) and the variable of integration (##x##). The integral must be rewritten to accurately reflect contributions from the entire rod, with the lower limit set at the left end of the rod. Participants encourage the use of LaTeX for posting equations to enhance clarity.

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athenad07
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Homework Statement
The charge per unit length on the thin rod shown here is What is the electric force on the point charge q? (See the preceding problem.)
Relevant Equations
here are the solution that I calculated, and I use the equation that E field equal to Force among charges over charges, but it yield quit different answer than the correct answer.
Screenshot 2024-10-27 at 15.14.04.png
Screenshot 2024-10-27 at 15.15.41.png
IMG_9426.JPG
IMG_9427.JPG
 
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This equation is set up incorrectly.

Screen Shot 2024-10-27 at 2.41.08 PM.png

  1. You are confusing the constant length of the rod ##l## with the variable of integration ##x##. You should keep the two separate and rewrite the integral.
  2. You want to add contributions from the entire rod, so the lower limit should be at the left end of the rod.
We would appreciate if you used LaTeX to post equations. To learn how, click on the link "LaTwX Guide", lower left, just above "Attach files."

(Edited for typos.)
 
Last edited:
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Okay! I will next time, thank you for the advice. Seems I still have a long way to learn :)
 
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athenad07 said:
Okay! I will next time, thank you for the advice. Seems I still have a long way to learn :)
Post your results when you're ready. We'll be here.
 
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