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Coulomb's Law and point charges

  1. Sep 16, 2014 #1
    Two m = 6.0g point charges on 1.0-m-long threads repel each other after being charged to q = 120nC , as shown in the figure.

    What is the angle θ? You can assume that θ is a small angle.

    25_P58.jpg

    Hopefully the image will work.

    I feel like something is missing. I've gotten 7.4 and 3.4 degrees - both wrong. I know the sum of the forces in all directions must equal zero. My equations then are:

    Fx = -Tsinθ+Felectric
    Fy = Tcosθ - mg

    We know m, g, and q. I know that coulomb's law is:

    F = Kq^2/r^2 ... but we don't know r.

    Any ideas?
     
  2. jcsd
  3. Sep 16, 2014 #2

    ZetaOfThree

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    You are given the length of the string and the angle. Do you see a right triangle you could make in order to determine r?
     
  4. Sep 16, 2014 #3
    Ah, yes ... a little clearer now.

    So sinθ = r/1 = r. Alright let me run with that. Let's see if I can get it now.

    Thanks for the nudge!
     
  5. Sep 16, 2014 #4

    ZetaOfThree

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    Wait! Are you sure ##\sin{\theta}=r##? Remember ##r## is the distance between the charges...
     
  6. Sep 16, 2014 #5
    When I replied, I realized I made a mistake, like you said. It's not r, but rather r/2!

    I was able to boil down the equation to:

    (sinθ)^2*(tanθ) = kq^2/(4mg)

    I'm pretty sure you can't boil it down anymore than that, so I used my old grapher to find the intersection point between both sides.

    Got it!

    Thanks a ton Zeta! I appreciate the insight!
     
  7. Sep 16, 2014 #6

    nrqed

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    You can actually do it withOUT using a graph. Note the hint: you may assume that the angle is small. In that approximation, what can you say about ## \tan \theta ## and ##\sin \theta ## ?
     
  8. Mar 10, 2017 #7
    Can you help? I worked through this and plugged my numbers in but when I try to solve for theta I don't get any kind of real number. Here's what I put in Wolfram Alpha:
    http://www.wolframalpha.com/input/?...*(8*10^-9)^2/(4*4*10^-3*9.8)+for+x+in+degrees

    Thanks!
     
  9. Mar 10, 2017 #8

    gneill

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    Staff: Mentor

    Wolfram says:

    upload_2017-3-10_4-10-49.png

    Can you explain those numbers? I recognize k and g but the rest is a mystery given the data in the problem statement of post #1.

    If you are actually working on a different problem with different data please start a new thread of your own. Hijacking old threads is against the rules.
     
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