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Homework Help: Non uniform surface charge density

  1. Jul 31, 2014 #1
    The problem is : A metallic horizontal disk of radius R has been charged on its top surface with a total charge Q such that its surface charge density is "non uniform" and governed by the expression σ=q|cosθ|*r where r and θ are the polar coordinates measured from the center O of the disk.
    Determine in terms of Q and R the value of q.
    I tried to solve it using double integral but it didn't work.
    σ=dq/ds then dq=q|cosθ|*r*rdrdθ then ∫dq/q=0R 02∏|cosθ|dθr2dr.
    If any body can help thanks.
  2. jcsd
  3. Jul 31, 2014 #2


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    Staff: Mentor

    I'm very rusty on this, but consider this ....

    In σ=q|cosθ|*r I think that q is fixed, so instead call it a constant, say, C.
    Leading to dq=C|cosθ|*r*rdrdθ then ∫dq=C 0R 02∏|cosθ|dθr2dr.

    You are solving for that constant C. If your textbook supplies the correct answer, does this get you closer?
  4. Jul 31, 2014 #3
    I think that leads to an answer,but the problem is that there is no answer in my text book.
    so I can't be sure about the answer.
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