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Work Done in Moving a Point Charge

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data
    Given that the electric field in a certain region is E = (z+1)*sin(Φ)aρ + (z+1)*ρ*cos(Φ)aΦ + ρ*sin(Φ)az V/m, determine the work done in moving a 4 nC charge from (4,0,0) to (4,30°,0).


    2. Relevant equations
    W = -Q*int(E·dl)


    3. The attempt at a solution
    Here is what I get:

    W = -4*int((z+1)*ρ*cos(Φ)*ρ*dΦ from 0 to 30°) nJ
    W = -4*(z+1)*ρ²*int(cos(Φ) from 0 to 30°) nJ
    W = -4*(0+1)*4²*(sin(Φ) from 0 to 30°) nJ
    W = -64*(sin(30°) - sin(0)) nJ
    W = -64*(.5 - 0) nJ
    W = -32 nJ

    The book, however, says the answer is -8 nJ. I get this answer when I leave off the ρ from the dl. This is how I think the answer in the book is found:

    W = -4*int((z+1)*ρ*cos(Φ)*dΦ from 0 to 30°) nJ
    W = -4*(z+1)*ρ*int(cos(Φ) from 0 to 30°) nJ
    W = -4*(0+1)*4*(sin(Φ) from 0 to 30°) nJ
    W = -16*(sin(30°) - sin(0)) nJ
    W = -16*(.5 - 0) nJ
    W = -8 nJ

    My question is: Is my answer the correct answer?
     
  2. jcsd
  3. Nov 1, 2009 #2

    Doc Al

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    Staff: Mentor

    Yes, I would say that your answer is correct.
     
  4. Nov 1, 2009 #3

    gabbagabbahey

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    Homework Helper
    Gold Member

    I agree with Doc; your answer is correct.:approve:
     
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