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What is the relationship between the maginitude of the radial electric field an

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data
    What is the relationship between the magnitude of a radial electric field and and its associated potential? Choose the correct general relationship?


    2. Relevant equations

    The following alternatives are given:
    a) E(r)= dV(r)/dr
    b) E(r)= V(r)/r
    c) E(r)= -dV(r)/dr
    d) E(r)= -V(r)/r

    3. The attempt at a solution

    I know the electric field is proportional to the inverse of (r^2) and the potential is proportional to the inverse of (r). My problem lies in understanding the calculus of the above formulas. Can anyone guide me through them please?
     
    Last edited: Oct 20, 2009
  2. jcsd
  3. Oct 20, 2009 #2

    Delphi51

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    Homework Helper

    Welcome to PF, physicsMad!
    Think of any electric field, not necessarily the one from a point charge.
    You have a tiny test charge q that you want to push from point A to point B. A is considered to have an electric potential of zero volts. What is the potential at B? By definition it is the work done (energy given) per unit charge to move q from A to B. So work is W = F*r where r is the distance or, since the F = qE may well be changing as you go,
    dW = F*dr = qE*dr for each little increment in distance dr
    The potential is the work done per charge or
    dV = dW/q = E*dr
    You can turn this around to get E = dV/dr.
     
  4. Oct 21, 2009 #3
    Thank you for the kind welcome Delphi51.

    I can now understand much better than before due to your explanation. I really appreciate it. However, i forgot to mention that the point charge has positive charge. So, the work would be negative the change occurs from higher potential to lower potential. Am I on the right track? If my thinking is correct, I would choose equation E(r)= -dV(r)/r.

    Thanks again :-)
     
    Last edited: Oct 21, 2009
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