Calculating Electric Potential on a Nonconducting Rod (2024)

  • Forums
  • Homework Help
  • Introductory Physics Homework Help
  • Thread starterDODGEVIPER13
  • Start date
  • Tags
    ElectricElectric potentialPotentialRod

In summary, you were trying to determine the potential at a point on a nonconducting rod by summing the potentials of all the charges at various distances from the origin. You plugged in the value for k and found that it was 2klamdaL. You then plugged in the answer for L and found that the potential at point P was 2klamdaL(log(sqrt(2L^2)+L)).

  • #1

DODGEVIPER13

672
0

Homework Statement

A nonconducting rod of length L = 6.00 cm and uniform linear charge density λ = +2.28 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 8.00 cm along the rod's perpendicular bisector?

heres the diagram best I could show it:
.P
|
|
|
|
<+++++++++++++++++++++>
<------L/2---|------L/2----->

Homework Equations

v=kq/r
lamda = charge/L

The Attempt at a Solution

What I did was this charge = L(lamda) the I said ∫kq/d ds which equals ∫klamda(L)/d * cos(theta) ds (where cos(theta)=d/sqrt(d^2+(L/2)^2)) so 2klamdaL∫1/sqrt(d^2+(L/2)^2) from 0 to L/2. which gives me 2klamdaL(log(sqrt(2L^2)+L) when I plug in the answer is incorrect I think my integral set up is completley incorrect?

Moderator note: Moved to the introductory physics forum.

Last edited by a moderator:

  • #2

DODGEVIPER13

672
0

My diagram is screwed up the .P with the line I made should be right over the little line seperating the L/2 lines sorry.

  • #3

Mindscrape

1,861
1

Are you saying your origin is in the middle of the rod or at the edge of the rod? You're kind of maybe on the right track. Remember that the basic concept is to make infinitesimal sums as you move along a charge distribution. Take a charge at a certain point from the origin and how that contributes to the potential, then move an infinitesimal amount and see how that new charge contributes.

  • #4

SammyS

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

11,935
1,527

DODGEVIPER13 said:

Homework Statement

A nonconducting rod of length L = 6.00 cm and uniform linear charge density λ = +2.28 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 8.00 cm along the rod's perpendicular bisector?

heres the diagram best I could show it:
.P
|
|
|
|
<+++++++++++++++++++++>
<------L/2---|------L/2----->

Homework Equations

v=kq/r
lamda = charge/L

The Attempt at a Solution

What I did was this charge = L(lamda) the I said ∫kq/d ds which equals ∫klamda(L)/d * cos(theta) ds (where cos(theta)=d/sqrt(d^2+(L/2)^2)) so 2klamdaL∫1/sqrt(d^2+(L/2)^2) from 0 to L/2. which gives me 2klamdaL(log(sqrt(2L^2)+L) when I plug in the answer is incorrect I think my integral set up is completley incorrect?

Moderator note: Moved to the introductory physics forum.


DODGEVIPER13 said:

My diagram is screwed up the .P with the line I made should be right over the little line separating the L/2 lines sorry.

Yes, no matter how many spaces you enter, the output only shows one space.

Use the "Codes" ikon to show something closer to what you want.

The "Codes box" actually displays in a mono-spaced font, so you still have to tweak it a bit.

Use some editor, like "Notepad" to format it like you want it to appear, or simoly count characters.

Code:

 .P | | | | <+++++++++++++++++++++++++++> <------L/2---|------L/2----->
  • #5

DODGEVIPER13

672
0

Ok so a test charge is positive and potential increase when moving close to a postive charge and I assume what you were saying is that from this I should be able to determine that is increasing at that infinitesmal movement toward that positive charge. but what does this tell me about how to set up the inetgral also the origin is in the middle.

  • #6

Mindscrape

1,861
1

Okay, now I know the geometry a bit better I can probably help more specifically. You've got your origin in the middle of the line and you are looking at a point above it, that's good because you've got some symmetry. Yeah, the idea is basically that a charge a certain distance from the middle (either right or left) will contribute a potential, or could also be an electric field (the idea is similar), to the point above the middle. If you had a single point a distance x' away you'd have

q/(x'^2+d^2)^(1/2)

see if you can generalize that to an integral form

  • #7

DODGEVIPER13

672
0

Thanks for the assist I got it sorry for the length of time to reply.

FAQ: Calculating Electric Potential on a Nonconducting Rod

1. What is electric potential?

Electric potential is a measure of the electrical potential energy per unit charge at a given point in space. It is also known as voltage.

2. How is electric potential calculated?

Electric potential is calculated by dividing the electric potential energy by the amount of charge present at a given point. It is measured in volts (V).

3. What is the electric potential over a rod?

The electric potential over a rod is a measure of the electric potential at different points along the length of the rod. It takes into account the distribution of charge along the rod and can be calculated using the equation V= kQ/x, where k is the Coulomb constant, Q is the charge on the rod, and x is the distance from the rod.

4. What factors affect the electric potential over a rod?

The electric potential over a rod is affected by the amount and distribution of charge on the rod, as well as the distance from the rod. It is also influenced by the presence of other charged objects or conductors in the surrounding space.

5. How does the electric potential change along the length of a rod?

The electric potential over a rod typically decreases as the distance from the rod increases. This is because the electric potential energy decreases as the distance between charges increases. However, the exact change in electric potential along the length of a rod depends on the distribution of charge along the rod and any external factors affecting the electric field.

Similar threads

MIT OCW, 8.02 Electromagnetism: Potential for an Electric Dipole

    Replies
    1
    Views
    2K

    Calculating eletric potential using line integral of electric field

      Replies
      1
      Views
      2K

      Potential due to a rod with a nonuniform charge density

        Replies
        2
        Views
        999

        Rod with Current on Rails in Magnetic Field

          Replies
          12
          Views
          552

          Disk with rod attached rotating about the center of the disk

            Replies
            13
            Views
            3K

            Potential and Electric Field near a Charged CD Disk

              Replies
              2
              Views
              949

              Find electric field a distance P from a charged rod

                Replies
                7
                Views
                2K

                Electric Potential inside an insulating sphere

                  Replies
                  11
                  Views
                  4K

                  How do you calculate Electric Potential Energy in a Square?

                    Replies
                    2
                    Views
                    3K

                    Potential difference between two points in an electric field

                      Replies
                      1
                      Views
                      2K
                      • Forums
                      • Homework Help
                      • Introductory Physics Homework Help
                      Calculating Electric Potential on a Nonconducting Rod (2024)
                      Top Articles
                      Latest Posts
                      Recommended Articles
                      Article information

                      Author: Moshe Kshlerin

                      Last Updated:

                      Views: 5438

                      Rating: 4.7 / 5 (57 voted)

                      Reviews: 80% of readers found this page helpful

                      Author information

                      Name: Moshe Kshlerin

                      Birthday: 1994-01-25

                      Address: Suite 609 315 Lupita Unions, Ronnieburgh, MI 62697

                      Phone: +2424755286529

                      Job: District Education Designer

                      Hobby: Yoga, Gunsmithing, Singing, 3D printing, Nordic skating, Soapmaking, Juggling

                      Introduction: My name is Moshe Kshlerin, I am a gleaming, attractive, outstanding, pleasant, delightful, outstanding, famous person who loves writing and wants to share my knowledge and understanding with you.