Electrostatics Line Charge question

[grandpa2390]

Homework Statement

Find the Electric field a distance z above one end of a straight line segment of length L that carries a uniform line charge λ

Homework Equations

Complicated formula due to lack of font for the notation used by the author of the book. so I wrote it out. I did my best to differentiate between the script r and pi.

just in case I did a terrible job, only the first "r" is pi, the rest are script r's

The Attempt at a Solution

My professor says during the lecture while doing this problem that the λ is not dependent on r so is a constant and can be pulled out of the integral, but then it also just disappears from the problem completely.

Why?

 

[cnh1995]

Your working is hard to read. It would be better if you typed the equations. You can use LaTeX.
https://www.physicsforums.com/help/latexhelp/

but then it also just disappears from the problem completely.

It shouldn't.
You need to first find the horizontal and vertical components of the field separately.

 

[haruspex]

but then it also just disappears from the problem completely.

Did your professor say that, or is it something you observe? It is still there in your final equation.

 

[Diegor]

Inside your integral there is a vector and it's magnitude is not 1 (as one can see in the drawing) so this magnitude will be there multiplying the argument and that is not right. You should be carefull when solving the integral.

Sorry i didn't see the hat over the u. That indicates that it is a unity vector.

 

[grandpa2390]

nvm
I got it.

 

[grandpa2390]

sry