# Calculating the resultant electric field

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1. Oct 12, 2016

### diredragon

1. The problem statement, all variables and given/known data
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. )

2. Relevant equations
3. The attempt at a solution

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.]

Last edited by a moderator: Oct 12, 2016
2. Oct 12, 2016

### Staff: Mentor

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.

Last edited: Oct 12, 2016
3. Oct 12, 2016

### diredragon

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. )

4. Oct 12, 2016

### 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