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Given an Electric Field find the necessary Work to move a charge Q

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Given the Electric field [tex]\vec{E}=z\vec{u_{x}}-3y^{2}\vec{u_{y}}+x\vec{u_{z}} V/m[/tex] find the necessary Work to move a charge [tex]Q=7\mu C[/tex] along an incremental path of [tex]1mm[/tex] distance in the direction of [tex]2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}}[/tex] wich locates in [tex]P(1,2,3)[/tex]

    2. Relevant equations
    Work
    [tex]W=-Q\int^{f}_{i}\vec{E}.d\vec{l}[/tex]
    i - inicial point
    f - final point
    Solution
    [tex]W=-75nJ[/tex]

    3. The attempt at a solution
    Converting to base units
    [tex]Q=7\mu C=7x10^{-6}C[/tex]
    [tex]d=1mm=1x10^{-3}m[/tex]
    The electric field at the given point
    [tex]\vec{E}=3\vec{u_{x}}-12\vec{u_{y}}+1\vec{u_{z}} V/m[/tex]
    The equation
    [tex]W=-Q\int^{f}_{i}\vec{E}.d\vec{l}=-Q.E\int^{f}_{i}dl.(2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}})[/tex]
    where [tex]\int^{f}_{i}dl=1x10^{-3}[/tex]
    My solution
    [tex]W=-525nJ[/tex]

    Where did I go wrong?
     
  2. jcsd
  3. Nov 14, 2009 #2
    You need to make dl a unit vector.
     
  4. Nov 14, 2009 #3
    Can't believe it was that simple. I'm embarrassed. Thank you!
     
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