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!

Electromagnetism - Potentials due to point charge and along line of of charge

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider an infinitely long and thin line of charge, with density 8nC/m. Calculate the electric potential difference ((phi)1-2) between two points in air at radial disances 1mm and 3mm.


    2. Relevant equations
    I am assuming:
    Phi(r) = λ/2(pi)ε0 * ln(rR/r) where rR is a reference point


    3. The attempt at a solution
    Our lecturer told us that we did not have to derive electric potential - just use what we had discussed in the notes, which, as far I can tell, is the above.

    As far as I can see, this is just plugging in 8x10^-9 c for λ, 3x10^-3m for rR, and 1x10^-3m for r.

    The problem: this is a 20 point question! One fifth of the assignment's points.

    I feel like there is something to this that I am missing, but, despite having poured through our notes and researched on the internet (and even found a worked problem that is similar), I cannot find anything else to do other than plug in for λ, rR, and r.

    If I'm wrong and there's a lot more I have to do, could someone please help point me in the right direction?

    1. The problem statement, all variables and given/known data
    The potential at position r due to a point charge q at position r' is

    phi(r) = q/4piε0 * 1/|r-r'|

    a.) Calculate grad phi and hence the electric field E.
    b.) What is the force experienced by a charge q1 at position r?
    c.) What is the potential energy of the charge at q1?

    2. Relevant equations
    Given above; however, also worth knowing is
    E = -grad phi
    U = q2 * phi

    3. The attempt at a solution
    This is like the above question, where, in my mind at least, the points allocated don't seem to match up with the amount of work to be done.

    Part a I have no problems with. I thought of r in terms of x,y, and z (again, according to our lecturer's advice), and then I used partial derivative with respect to x, then stated that, according to symmetry, y and z worked out to be the same, giving an answer of
    grad phi = q/4piε0 * r'-r/|r-r'|^3

    and since E = -grad phi, this reversed the top value (r'-r) to give
    E = = q/4piε0 * r-r'/|r-r'|^3.

    That felt like a solid 10 points worth of work.

    To do part b, it seems that all I have to do is multiply another q into the equation, and multiply that by -1 (since the charge is going from q1 (which I assume is equivalent to "q2") to q (which I assume is equivalent to "q1")). This feels more like 2 or 3 points worth of work.

    Then for part c, I have done a negative integral of what I calculated for F, with respect to r. This gives me

    U = q*q1/4piε0 * 1/|r-r'|

    Not only does this answer not seem correct, but it also doesn't feel like 10 points worth of work.

    Again, if someone could help me see where I went wrong, and point me in the direction of whatever I'm missing, I would be very grateful.

    Thanks!
     
  2. jcsd
  3. Oct 26, 2011 #2
    All of that seems correct....
    Probably the teacher expected you to calculate the potential in the first question. But it is good what you have done.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Electromagnetism - Potentials due to point charge and along line of of charge
Loading...