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The relation between Electric Field and Electric Potential

  1. Jul 1, 2016 #1
    1. The problem statement, all variables and given/known data

    The electric field and the electric potential at a point are E and V respectively.
    (a) If E=0, V must be 0
    (b) If V=0, E must be 0
    (c) If E≠0, V cannot be 0
    (d) If V≠0, E cannot be 0

    2. Relevant equations

    E = V/d

    3. The attempt at a solution

    I basically substituted the value of E and V as 0 in respective cases, but ended up getting (a) and (b) as true. I know this is a very fundamental question, but I just can't figure it out.
     
  2. jcsd
  3. Jul 1, 2016 #2

    cnh1995

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    In your question, V is the absolute potential at the given point while electric field E=potential difference/d.
     
  4. Jul 1, 2016 #3

    SammyS

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    Does any one of them have to be true?

    It looks like there are pairs of them which are logically equivalent.
     
  5. Jul 1, 2016 #4

    Charles Link

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    Te electric field E and electric potential V are two separate functions. Although the potential depends on the electric field, they are not proportional and the potential depends on the integral of the electric field over a path. The forum rules don't allow simply giving the answer, but the answer is quite simple. @SammyS The pairs are not logically equivalent. The equation the OP presents that E=V/d does have precise proportionality between E and V, but this equation is very misleading because it does not apply in general. It is for the special case of an ideal capacitor and E is the uniform electric field between the plates and V is the voltage drop across the plates. The equation really does not apply here, and the capacitor equation does not give V at any location between the plates where the E field is present. Although it looks like the right equation, it is totally irrelevant to this problem.
     
    Last edited: Jul 1, 2016
  6. Jul 1, 2016 #5

    SammyS

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    Are you saying that there is no pair that are not logically equivalent?

    From a pure logic point of view.

    (P implies Q) is logically equivalent to ((not Q) implies (not P)) .

    It appears to me that we can find cases where one of these statements is the contrapositive of another.
     
  7. Jul 1, 2016 #6

    Charles Link

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    @SammyS It is somewhat difficult to answer your question without giving out the complete answer (at least what I am pretty certain is the correct answer), but none of the statements contains logical equivalence. To just give a counterexample for statement "d", a charged hollow conducting sphere has E=0 throughout the entire interior, but V is not equal to zero.... editing.. And to give the OP something that might help them answer "b" and "c", what is the V and E for the point midway between two electrical charges of +Q and -Q? And I think the example I gave for "d" can also be used to answer "a".
     
    Last edited: Jul 1, 2016
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