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Derivation for E = V/d? (capacitors)

  1. May 3, 2012 #1
    One of the formulas I came across while doing problems with simple parallel plate capacitors was E = V/d, where E is the magnitude of the electric field between the plates, V is the potential difference between the plates, and d is the separation of the plates. I'm wondering where this formula is derived from.

    I know that the electric field between the two plates of a capacitor is constant (except near the edges), but am not sure how that would play into the explanation.
  2. jcsd
  3. May 3, 2012 #2


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    Science Advisor

    Think of the definitions of electric field and electric potential, and then think of W = F d.
  4. May 3, 2012 #3
    well the definition of an electric field is F/q, where q is in the field, and the definition of electric potential is electrical potential energy divided by charge.

    E = F/q
    V = E/q
    W = Fd

    So by substitution, W = Eqd

    I want to get to E = V/d so I'll solve for E...

    E = W/qd

    So W/q is somehow equal to V? So W/q = E/q

    And by the work energy theorem, W = delta E, and the voltage in E = V/d is in fact a potential difference.

    Thanks! I literally reasoned that out while typing. Thanks for pointing me in the right direction.
  5. May 3, 2012 #4


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    Staff: Mentor

    Like you said at the beginning of your post... :biggrin:
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