Electric field caused by a uniform linear charge

[gotem3303]

A uniform linear charge density of $$\lambda$$ = 2.0 nC/m is distributed along the x-axis from x = 0 to x =3m. Which integral is correct for the magnitude of the electric field at x = -4 m on the x axis?
I'm going over a old test and he didn't circle the correct answer but I'm trying to understand the denominator.
I'm pretty sure I have everything but the denominator, would it be $$\int$$$$\frac{18dx}{(4+x)^{2}}$$ from 0 to 3?

 

[Redbelly98]

Looks okay, except that you did not write any of the units.

 

[thomate1]

Yes, that is the correct integral for the magnitude of the electric field at x = -4 m on the x-axis. The denominator represents the distance from the point where the electric field is being measured (x = -4 m) to the point where the linear charge density begins (x = 0). This distance is (4 + x), and since x = -4 m, the distance becomes (4 - 4) = 0. Therefore, the integral becomes \int\frac{18dx}{0^{2}} from 0 to 3, which is undefined. This makes sense since at x = -4 m, the point is located within the distribution of the linear charge density, so the electric field would be infinite.