Find the Potential as a function of position

Click For Summary
SUMMARY

The discussion focuses on calculating the electric potential V as a function of position along the x-axis due to a uniformly charged rod of length L and total charge Q, positioned along the y-axis. The relevant equations include the differential potential dV = \vec{E} \cdotp d\vec{l} and the potential formula V = \frac{kq}{r}. To solve the problem, one must integrate the potential contributions from each infinitesimal charge element dq along the rod, using the relationship between the coordinates and applying Pythagorean theorem to express r in terms of x and y.

PREREQUISITES
  • Understanding of electric potential and electric fields
  • Familiarity with calculus, specifically integration
  • Knowledge of charge distribution concepts
  • Basic understanding of coordinate systems in physics
NEXT STEPS
  • Study the integration of electric potential for different charge distributions
  • Learn about the application of Pythagorean theorem in physics problems
  • Explore the concept of electric field (E) and its relation to potential (V)
  • Review examples of calculating potential from continuous charge distributions
USEFUL FOR

Students in physics, particularly those studying electromagnetism, as well as educators looking for examples of electric potential calculations involving continuous charge distributions.

prace
Messages
99
Reaction score
0

Homework Statement


A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis


Homework Equations


[tex]dV=\vec{E}\cdotp d\vec{l}[/tex]

[tex]V=\frac{kq}{r}[/tex]


The Attempt at a Solution



I think I am to use the first equation posted, but I am not sure how to relate it to the x-axis, if the rod lies along the y-axis. Also, what is the displacement here? I am assuming it is just dy?
 
Physics news on Phys.org
prace said:

Homework Statement


A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis

Homework Equations


[tex]dV=\vec{E}\cdotp d\vec{l}[/tex]

[tex]V=\frac{kq}{r}[/tex]

The Attempt at a Solution



I think I am to use the first equation posted, but I am not sure how to relate it to the x-axis, if the rod lies along the y-axis. Also, what is the displacement here? I am assuming it is just dy?
You have to integrate along the rod from y = 0 to +L.

[tex]V(x) = \int_{0}^{L} \frac{k}{r}dq[/tex]

Work out the expression for dq in terms of dy. Work out the expression for r in terms of x and y (think: Pythagoras).

AM
 
Last edited:

Similar threads

Replies
1
Views
3K
  • · Replies 16 ·
Replies
16
Views
2K
Replies
5
Views
1K
Replies
64
Views
6K
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 20 ·
Replies
20
Views
7K