Asymmetric Line Charge Voltage

[PlatoDescartes]

Homework Statement

A line of charge with a non-uniform charge density lambda=ay, where a=−34.00 nC/m^2 lies along the y axis in the region 0≤y≤2.90 m. Calculate the electric potential of this line of charge at point P on the x axis a distance 0.80 m from the origin. Assume the potential equals zero at infinity.

The given picture is of a line of charge along the y axis, of h length, with a point charge P, d=0.8m distance away from the line of charge.

Homework Equations

∆V = VB −VA = the negative integral E dl from a to b where
E=-dV
dV=kdQ/r
dQ=lambdadl[/B]

The Attempt at a Solution

To start, I used dQ=lamdadl=34nC/m^2 (y)dl. I substituted this in for dQ in dV, which I substituted into E in the integral. From there, I end up with the integral of k(34 x 10^-9)ydy/.8 from 0 to 2.9. Solving this equation though does not yield the correct answer and therefore I would appreciate some assistance.

CORRECTION: The above work is an attempt to find the total charge, which was not clearly stated beforehand. Sorry.[/B]

 

[haruspex]

Homework Statement

A line of charge with a non-uniform charge density lambda=ay, where a=−34[PLAIN]http://lc1.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3A.png00 nC[PLAIN]http://lc1.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3D.pngm^2 lies along the y axis in the region 0<y<2[PLAIN]http://lc1.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3A.png90 m. Calculate the electric potential of this line of charge at point P on the x axis a distance 0.80 m from the origin. Assume the potential equals zero at infinity

Homework Equations

∆V = VB −VA = the negative integral E dl from a to b where
E=-dV
dV=kdQ/r
dQ=lambdadl[/B]

The Attempt at a Solution

To start, I used dQ=lamdadl=34nC/m^2 (y)dl. I substituted this in for dQ in dV, which I substituted into E in the integral. From there, I end up with the integral of k(34 x 10^-9)ydy/.8 from 0 to 2.9. Solving this equation though does not yield the correct answer and therefore I would appreciate some assistance. [/B]

We cannot usually tell where you went wrong if you do not post your working.

 

[PlatoDescartes]

We cannot usually tell where you went wrong if you do not post your working.

I apologize for evidently not being clear enough.
I used the equations that I stated in the relevant equations and, substituting information as stated in the attempt at a solution, and came up with ∫(k(34*10^-9)ydy)/.8 which, before being evaluated from 0 to 2.9, equals k(34*10^-9)y^2/2, with a final answer of 1606.6C, which is incorrect. Is that not enough of an explanation..?

 

[haruspex]

CORRECTION: The above work is an attempt to find the total charge,

That explains why I thought there was a lot more working to show. The question asks for a potential.

came up with ∫(k(34*10^-9)ydy)/.8

Now I'm really confused. Why do you care about k or the distance to P if you are only trying to calculate the total charge?
Looks like you are intending to treat all the charge as though it is located at the origin, but it isn't.
For the element dy, what potential does it create at P?

 

[PlatoDescartes]

That explains why I thought there was a lot more working to show. The question asks for a potential.

Now I'm really confused. Why do you care about k or the distance to P if you are only trying to calculate the total charge?
Looks like you are intending to treat all the charge as though it is located at the origin, but it isn't.
For the element dy, what potential does it create at P?

Yup, I was pathetically and ridiculously confused too; my error lied in misreading problem statements. I am very sorry about that. To find total charge, dQ=λdl, which in this case dQ=-34*10^-9ydy. Integrate with respect to y from 0 to 2.9 and you get -34*10^-9(2.9^2)/2, which yields the correct answer.

If you can bear with me for another question, I want to double check how to find the electric potential of the line of charge at point P (distance .8m along x axis). For this, I would use kq/r, but would I still need to use integration after having found q?

 

[haruspex]

I would use kq/r, but would I still need to use integration after having found q?

Not entirely sure what you mean by that.
By "having found q", you seem to be referring to total charge. That is of no use in trying to find the potential at P because the various bits of the charge are at different distances from P. You need to start again with the charge in an element dy, find what that contributes to the potential at P, and integrate that.

 

[PlatoDescartes]

Not entirely sure what you mean by that.
By "having found q", you seem to be referring to total charge. That is of no use in trying to find the potential at P because the various bits of the charge are at different distances from P. You need to start again with the charge in an element dy, find what that contributes to the potential at P, and integrate that.

I understand. Thanks for your help.