How to Calculate the Electric Field Near a Long Charged Wire?

[K3nt70]

Homework Statement

Calculate the electric field at a point 2.00 cm perpendicular to the midpoint of a 1.94 m long thin wire carrying a total charge of 4.78 uC.

Hint: You could integrate BUT if the wire is very long compared to the distance from the wire to where you are calculating the electric field, then the electric field will be radial and Gauss's law might be easier.

Homework Equations

E = $$\frac{kq}{r^2}$$

where k = 9E9
q = 4.78E-6
r = 0.02 m

E = $$\frac{kQx}{(x^2 + a^2)^(3/2)}$$

The Attempt at a Solution

First i tried to use the second formula where i made the wire into a circle and used 0.02m as the radius. That didnt work, so i used gauss's formula as the hint suggests, which also didnt work. Suggestions?

 

[K3nt70]

Nevermind, i solved it.