What is the Electric Potential of a Uniformly Charged Bent Wire?

[Leeoku]

Homework Statement

. A wire of finite length that has a uniform linear charge density
λ=6.22×10-9 C/m is bent into the shape shown below.
[PLAIN]http://lulzimg.com/i23/7498af.jpg
Answer: 2.98e+02 V

Homework Equations

V = k integral (dq/r)

The Attempt at a Solution

So i think my integrals are right not sure. I have to split into line and circle.
Left line: K (integral -3r->-R) lambda dx/x
Circle: K (integral -pi->0) lambda d theta
Right line k(Integral R->3R) lambda dx/x

So when i integrate and plug stuff in i get
K*Lambda (ln[-R]-ln[-3r]+pi+ln[3R]-ln[R])
im not sure how to simplify the terms with ln R

side note: How can i properly write stuff out on forums? =S

 

[ideasrule]

So i think my integrals are right not sure. I have to split into line and circle.
Left line: K (integral -3r->-R) lambda dx/x

This isn't right. In V = k integral (dq/r), r is the distance between the charge and the origin, and can't be negative.

Circle: K (integral -pi->0) lambda d theta
Right line k(Integral R->3R) lambda dx/x

These are right.

So when i integrate and plug stuff in i get
K*Lambda (ln[-R]-ln[-3r]+pi+ln[3R]-ln[R])
im not sure how to simplify the terms with ln R

You can use the identity ln(a)+ln(b)=ln(a*b), or equivalently, ln(a)-ln(b)=ln(a/b).

side note: How can i properly write stuff out on forums? =S

The usual way is to use LaTex. See here for a tutorial: http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/

For most purposes, you can just search up and use Unicode symbols along with the exponent and underscore tags. There are text symbols for all the Greek characters, for some fractions, for the integral sign, and probably for a lot more things I don't know about.

 

[Leeoku]

i don't understand what to integrate from the left side. How am i supposed to express it with relation to the origin or do i just take the right integral and multiply by 2?