Hvae a look at the diagram(adsbygoogle = window.adsbygoogle || []).push({});

Caluclate the force on the point charge q, due to a uniformly charged rod of length L a distance x from the point charge q. Discuss the limit when L approaches infinity with lambda = Q/L fixed.

[tex] Q = \lambda L [/tex]

[tex] dQ = \lambda dL [/tex]

Force of dQ on the point charge q is given by

[tex] dF = \frac{1}{4 \pi \epsilon_{0}} \frac{qdQ}{(L+x-s)^2} [/tex]

no Y components since the rod is thin. SO this force is the total force in the horizontal direction only.

[tex] F = \int dF = \int_{s=0}^{s=L} \frac{1}{4 \pi \epsilon_{0}} \frac{q \lambda ds}{(L+x-s)^2} [/tex]

[tex] F = \frac{q \lambda L}{4 \pi \epsilon_{0}} \frac{1}{x(L+x)}[/tex]

[tex] F = \frac{Qq}{4 \pi \epsilon_{0} x(L+x)} [/tex]

now for the limit where L -> infinity

i used L'Hopital's Rule and got the answer to be zero. But i find it hard to believe that that is the case. I Would think that this has something to di wth the limtis of integration being s=0 to s=infinity

im not sure however... do help

thank you in advance for your help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Force on a point charge due to a rod

**Physics Forums | Science Articles, Homework Help, Discussion**