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!

Homework Help: Find the net force on charge

  1. Apr 25, 2012 #1
    1. The problem statement, all variables and given/known data
    13 equal charges are placed in the corners of a regular 13-sided polygon. What is the force on a test chrage at the center?

    2. Relevant equations
    principle of superposition

    3. The attempt at a solution
    I am not sure if the net force is 0 or not. Had the polygon been 12-sided the symmetry would be obvious, but I'm not sure in this case. Can anyone explain if the net force is 0 or not?
  2. jcsd
  3. Apr 25, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi aaaa202! :smile:
    try it first for an equilateral triangle (3 equal charges) …

    is that 0 ?​

    then use the same method for 13 (you'll need a formula for summing a trig series)
  4. Apr 25, 2012 #3
    Did the calculations for a triangle as you said, where i fixed the coordinates such that one of the charges sat on the y-axis. From there it was easy to see that Fres = 0, and I think that this must hold for any rotation of the coordinate system. After all I think the length of a vector is more or less defined to be preserved on a rotation in the euclidean coordinate system. However, I'm not sure, so can you confirm this? :/
    And can you perhaps come up with a symmetry argument that makes it easy to see, that rotation of the coordinate system should not change the lFresl? :)
  5. Apr 25, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper


    presumably you did cos0 + cos2π/3 + cos4π/3 = 1 - 1/2 - 1/2 = 0 ?

    ok you now need to prove cos0 + cos2π/13 + cos4π/13 + … cos24π/13 = 0 :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook