(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi, I need to figure out what happens to this equation in the limits

[tex] E = \frac{1}{4\pi\epsilon_0} \frac{2\lambda L}{z \sqrt{z^2+L^2}} [/tex]

in the two different cases

that z>>L

and when L -> infinity

(note this equation was derived from finding the electric field da distance z, above the midpoint of a straight line segment of length 2L, which carries a uniform line charge of [tex] \lambda [/tex]

3. The attempt at a solution

for the case when, z>>L I can see how the L term becomes insignificant in the square root on the bottom,

and so the equation would just become

[tex]\frac{1}{4\pi\epsilon_0} \frac{2\lambda L}{z^2} [/tex]

but for the case when L approaches infinity, what do I do???

the squareroot of a L^2 +z^2 == L?

does that mean the L can just be canceled out?

[tex] \frac{1}{4\pi\epsilon_0} \frac{2\lambda L}{z *L} [/tex]

and the equation becomes?

[tex] \frac{1}{4\pi\epsilon_0} \frac{2\lambda}{z} [/tex]

i'm not sure if i'm allowed to since the Z was the distance from the midpoint of the line,

the first one makes sense since it just becomes a point charge of 2lambda L

but the second case, i'm not too sure what it becomes

**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!

# Homework Help: Limits and infinity problem

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