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

1. Feb 4, 2010

### JJBladester

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

1. The problem statement, all variables and given/known data

What is the limit of the following equation?

2. Relevant equations

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

3. 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.

2. Feb 4, 2010

### Dick

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

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.

3. Feb 5, 2010

### JJBladester

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

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 :)

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