Potential of a non-uniform charged rod

  • Thread starter AJDangles
  • Start date
  • #1
48
0

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).
 

Answers and Replies

  • #2
48
0
Diagram and work:
 
  • #3
48
0
Sorry. Here is the diagram and work:
 
  • #5
ehild
Homework Helper
15,525
1,901
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
 
Last edited:
  • #6
55
0
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
 
Last edited:

Related Threads on Potential of a non-uniform charged rod

Replies
1
Views
2K
Replies
2
Views
3K
Replies
15
Views
8K
Replies
9
Views
15K
Replies
1
Views
1K
Replies
9
Views
2K
  • Last Post
Replies
5
Views
10K
Replies
7
Views
4K
Top