Calculating the resultant electric field

[diredragon]

Homework Statement

In the picture below it is asked that i calculate the resultant electric field if the linear charge density is known.

Calculate the resultant electric field of a charged semicircle wire (positioned as in the picture) at some point M on the Z axis if the linear charge density of the wire is known ( wire is thought to be infinetly thin. )

Homework Equations

3. The Attempt at a Solution [/B]
I calculated the projections but the part ( which i circled ) is the solution from the book. That has to be wrong right? When we replace the linear charge density expression the π is squared not lost?[Mentor note: Added OP's text description of the problem statement, moved the image to be inside the problem statement section.]

 

[gneill]

Can you provide a text description of the problem statement please? Helpers shouldn't have to decipher your math to understand the layout of the charge distribution under consideration.

Update: I massaged the problem statement to include the description provided by the OP.

 

[diredragon]

Can you provide a text description of the problem statement please? Helpers shouldn't have to decipher your math to understand the layout of the charge distribution under consideration.

Ok sorry xD...Calculate the resultant electric field of a charged semicircle wire (positioned as in the picture) at some point M on the Z axis if the linear charge density of the wire is known ( wire is thought to be infinetly thin. )

 

[Simon Bridge]

Looks like a circular line of total charge ##Q##... radius ##a## ... so charge density ##\lambda = Q/2\pi a##
[edit - no it is a semi-circle ... then charge density is ##Q/\pi a## - you wrote the other]
The task is to find the field on the z axis... is this correct?
However, you spend a lot of time apparently looking for ##E_x##
[edit: explains the time to find the x component]

See example:
http://www.phys.uri.edu/gerhard/PHY204/tsl329.pdf