Limit Problem - Electric field strength of an infinite line of charge

[JJBladester]

Limit Problem --- Electric field strength of an infinite line of charge

Homework Statement

What is the limit of the following equation?

Homework Equations

$$\stackrel{lim}{L\rightarrow\infty} \frac{K|Q|}{r\sqrt{r^{2}+(L/2)^{2}}}$$

The Attempt at a Solution

The book gives an answer of $$\frac{K|Q|}{rL/2}$$ but it doesn't explain the intermediate steps.

K is a constant, Q represents charge, L represents length, and r represents distance from a wire to a point in space. The whole exercise is to see what happens to the electric field strength of the wire if its length is allowed to grow infinitely.

 

[Dick]

Factor the L^2 out of the expression in the square root. So sqrt(r^2+(L/2)^2)=sqrt(L^2(r^2/L^2+1/4)=sqrt(L^2)*sqrt((r/L)^2+1/4)=L*sqrt((r/L)^2+1/4). Now as L->infinity, r/L goes to zero.

 

[JJBladester]

Dick,

Thanks for your response. The first sentence you made helped me get through it!

Factor the L^2 out of the expression in the square root... I guess the more problems I do, the more my math intuition will increase. On that note, I found a site www.betterexplained.com that has really helped me conceptualize things like "what is a limit" without a cheesy explanation like "the area under the curve". Check it out :)