1. Not finding help here? Sign up for a free 30min 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!

Beam of particles in a cylindrical pipe

  1. Apr 26, 2013 #1

    CAF123

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Charged particles, each holding charge q are moving in a cylinderical beam centred on the x-axis with n particles per unit volume. All the particles have the same horizontal velocity v.

    A) By considering a suitable Gaussian surface, calculate the E-field as a function of r, the radial distance from the x-axis, and hence the force on the charges particle due to the electric field.

    2. Relevant Equations

    Gauss Law,

    3. The attempt at a solution

    Let a be the radius of the pipe. Choose a Gaussian cylinder to be of radius r < a. Then the E field (from the enclosed charge) and the dA elements are parallel, so by Gauss,## E∫dA = Q_{enc}/ε = E(2 \pi r h),## h the height of the pipe and Gaussian cylinder.

    I then said that the volume charge density is ##Q/\pi a^2 h##. So in the Gaussian cylinder, the charge enclosed is ##(\pi r^2 h) \cdot Q/\pi a^2 h = \left(\frac{r}{a}\right)^2 nq## which then gives me the E field and hence the force. My problem is, when I checked the solutions, they say the charge enclosed is ##Q = nq \pi r^2 h## and then they get an E field of ##nrq/2\epsilon##. To be honest, I think this is wrong. This expression for Q yields incorrect dimensions and then when they calculate the E field, they have ##Nm^3/C## which again is wrong. Both my expressions give the correct dimensions. Am I correct?

    Many thanks.
     
  2. jcsd
  3. Apr 26, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi CAF123! :smile:
    I don't understand …

    q is charge, n is 1/volume
     
  4. Apr 26, 2013 #3

    CAF123

    User Avatar
    Gold Member

    Yes, there are n particles per unit volume so charge of nq per unit volume. So (volume) charge density is ##nq/(\pi a^2 h)##. Then I multipled this by the volume of the Gaussian cylinder to get the charge within the Gaussian cylinder.
     
  5. Apr 26, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    No, there's a charge of nq per m3.

    Volume of cylinder = πa2h m3, so total charge in cylinder = πa2hnq,
    and charge inside radius r = πr2hnq
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Beam of particles in a cylindrical pipe
  1. Cylindrical Capacitor (Replies: 3)

Loading...