1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Potential at the end of a rod

  1. Jul 26, 2012 #1
    Hi all!

    So I've been doing some work with potential calculations, and I seem to be running into a bit of trouble with figuring out how to think about the potential due to a rod at the very edge of it.

    Imagine an insulating rod with charge Q is placed along the positive x-axis, with its left end at the origin. I can calculate the potential anywhere on the y-axis, and anywhere on the negative x-axis quite easily. But when I try to take the limiting case of a point at the left end of the rod, something strange happens: I can let y approach 0, or x approach 0 in either of the expressions, and I find that the potential at the end of the rod is infinite. This is because the potential contains the natural log.

    I contend that this doesn't make physical sense! You see, what if I had instead charged the rod to a charge Q+q. If the potential when charge Q is already on the rod is infinite at the end, how can I place the extra bit q on the rod? But I know that Q can have any value, which means I should be able to make Q large enough that it includes that extra bit, had I wanted to from the start.
     
  2. jcsd
  3. Jul 26, 2012 #2

    Drakkith

    User Avatar

    Staff: Mentor

    I don't understand. Why are you trying to find the potential between 2 points on the rod if the rod is charged with Q? Wouldn't there be 0 potential?
     
  4. Jul 26, 2012 #3
    I think not- for one, it's not a conductor, and for two this is relative to a 0 potential at infinity, the way that I'm thinking about it (I'm integrating dV over the entire rod to get V, but this all presupposes that V=0 at infinite distances).
     
  5. Jul 26, 2012 #4

    Drakkith

    User Avatar

    Staff: Mentor

    Do you have a charge on the end of the rod, or is the whole rod charged?
     
  6. Jul 27, 2012 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The defiance of physical sense reflects the unreality of the model. A uniform charge over a one-dimensional manifold will always produce infinite potential on the manifold itself.
    To avoid this you need to make it at least 2 dimensional, but might as well make it 3. 5.8.7 in http://www.astro.uvic.ca/~tatum/celmechs/celm5.pdf derives the (gravitational) potential due to a uniform solid cylinder.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Potential at the end of a rod
Loading...