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Homework Help: Electric Potentials (4 charges on corners of a rectangle)

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data

    A rectangle has sides of length 5cm (right and left) and 15cm (top and bottom).

    Top left corner has charge (q1) = -5uC
    Top right corner has charge A = ?
    Bottom left corner has charge B = ?
    Bottom right corner has charge (q2) = 2uC

    a) What are the electric potentials of A and B
    b)How much external work is required to move a third charge (q3 = 3uC) from B to A along the diagonal of the rectangle

    2. Relevant equations

    Not too sure. For part b I'm thinking I would use a line intergral and say that the diagonal path from A to B is equivilent to going from B to q1, then q1 to A.

    V = U/Qo

    But where will I get U (potential energy) from?



    3. The attempt at a solution

    What I really want is part a, once part a is done I can just do some line intergrals to find the work done for part b.

    Do I use equipotentials? So potential of A is the same as potential of q1? B is the same as q2?

    Any pointers and I'm very grateful.
     
  2. jcsd
  3. Mar 29, 2010 #2
    Calculate the potential due to a point charge as a function of distance. The potentials add at any given point in space. How is the electric field created by a point charge related to the potential?
     
  4. Mar 29, 2010 #3
    I'm still confused sorry. Say if I wanted to find the potential of A, which is in the top right corner. It is inbetween two different fields created by charges q1 and q2. I cannot just find the electric field of one, then say 'since A is a distance r from this charge it's potential is this'??? It doesn't make sense. Don't fields superimpose?

    And the fact that I'm working with a damn rectangle makes it more harder to interpretate.

    Please, more help :(
     
  5. Mar 29, 2010 #4
    Electric field of q1 at B: -1.8E7 Nc-1
    Electric field of q1 at A: -2E6 Nc-1
    Electric field of q2 at B: 8E5 Nc-1
    Electric field of q2 at A: 7.2E6 Nc-1

    K so these are the electric fields using the distances on the rectangle. Now to find the potentials of A and B, how to do this?
     
  6. Mar 29, 2010 #5
    K, A and B are just corners... Hmm..
     
  7. Mar 29, 2010 #6
    Electric fields superimpose and so do potentials. Potentials are scalars so the superposition is straightforward. You should be able to find the potential of a point charge anywhere in space from

    [tex]V=-\int^r_\infty\vec{E}\cdot\mbox{d}\vec{r'}[/tex]

    and Gauss's Law can be used to find the E field of a point charge as a function of r. The upper limit r is the distance from the point charge to a corner.
     
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