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

1. Feb 4, 2010

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