Find net electric field in a wire?

[saba.shahin95]

After solving this problem I ended up with--(2a is the length of the wire)(integral limit is from -a to +a)
(x is the ⊥ distance from centre of the wire to a point P where we have to find the net field )
E[SUBx]= (1/4Πε)*(Q/2a)∫x.dy/(x^2+y^2)^3/2

P.S- sorry, I'm not able to upload the image of the problem. This is my first time ever at this site.
Help me in solving this integral.
Detailed solution would be appreciated . ☺

 

[mfb]

That's an integral you can look up. WolframAlpha knows it, too and it even shows the relevant steps for free.

 

[STEMucator]

Do you want the electric field in the wire or around the wire at some point in space $P$? I'm assuming you want the electric field at some point $P$.

The easiest way to do this problem is to position the wire along the z-axis and enclose it in a cylindrical Gaussian surface. Then using Gauss' law, find the magnitude of the electric flux density $| \vec D |$ in terms of the enclosed charge.

Then using $\vec D = \varepsilon \vec E$, you will be able to find the electric field.

Hint: The electric flux density $\vec D$ points radially outwards from the cylinder, so in cylindrical co-ordinates we can write it as $\vec D = |\vec D| \hat r$.