Potential of a non-uniform charged rod

[AJDangles]

Homework Statement

A thin charged rod of length L lies along the x-axis as shown in the diagram below.
The charge on the rod is distributed with a density of λ= c x (C /m) where c is a constant.

What is the potential at a point (0,y)? (Your answer should be in terms k, c, L, and y).

See attached pictures for attempt at solution and diagram.

What I'm having trouble with is determining where to sub in λ = cx. Also, I'm not sure how to derive the potential at the point, but I think what I have derived there without solving the integral is the electric field at that point. Also, I don't know how to evaluate the integral (I've never taken a uni-level calc course.. but i know how to do basic u substitution and trig subs if that's what is needed).

 

[AJDangles]

Diagram and work:

 

[AJDangles]

Sorry. Here is the diagram and work:

 

[AJDangles]

Wow, fail. K here it is last time lol:

 

[ehild]

Hi AJDangles,

Read the problem again: it asks the potential. Do you know what is the potential of a point-like charge dq at the point shown in the figure?
(The potential is a scalar quantity. At distance R from a point charge Q it is V=kQ/R. )

You are given the linear charge density, λ. It means that the charge of a small piece of length dx is dq=λdx. Substitute λ=Cx.

Take care, the charge density is of opposite sign for negative x values than for the positive ones.


ehild

 

[hansbahia]

You are given the linear charge density, λ. It means that the charge of a small piece of length dx is dq=λdx. Substitute λ=Cx.

Take care, the charge density is of opposite sign for negative x values than for the positive ones.

Lets say λ= constant c times x³
λ= cx³
I integrated from 0 to a
so
Q=∫cxdx
Q= ca⁴/4

How can I find c?
Can I set Q=0?
The reason I'm asking is because my assignment ask me to find the total dipole moment