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Electric potential in a uniform electric field please help

  1. Nov 7, 2004 #1
    k im really confused about how to go about setting up the intergral of Eds. how do u choose the limits of integration and how do u know whether to write Va-Vb= -(integral) E ds
    or Vb-Va = - (integral) E ds

    its really frustrating me
    i thought i understood but i realised i really dont
    my teacher said something about choosing the direction of ds to be the same as the e field..but that doesnt help me much
    im just confused

    itd be really cool if someone could straighten this out
    Last edited: Nov 7, 2004
  2. jcsd
  3. Nov 7, 2004 #2


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    Science Advisor
    Homework Helper

    First, realize that

    [tex]\vec E = - \nabla V[/tex]

    (note the minus sign) and

    [tex]\int_a^b \nabla V \cdot d\vec s = -\int_a^b \vec E \cdot d\vec s[/tex]


    [tex]V(b) - V(a) = -\int_a^b \vec E \cdot d \vec s[/tex]

    so your E ds is really [itex]\vec E \cdot d \vec s[/itex]

    That's what determines your signs.
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