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Potential Difference

  1. Mar 5, 2009 #1
    I am wondering if I did this right.

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

    What is the potential difference between the points (x_i, y_i) = (0cm, -5cm) and (x_f, y_f) = (1cm, 4cm) in a uniform electric field equal to E = (20000i - 50000j) V/m ?

    2. Relevant equations

    [tex]\Delta V = V(s_{f})-V(s_{i}) = -\int^{s_{f}}_{s_{i}}E_{s}ds[/tex]

    E is uniform therefore:

    [tex]\Delta V = - E_{s}\Delta s[/tex]

    [tex]\Delta s = \sqrt{(9cm)^{2}+(1cm)^{2}}[/tex]

    [tex]= \frac{\sqrt{82}}{100} m[/tex]

    [tex]E = \sqrt{(20000V/m)^{2}+(-50000V/m)^{2}}[/tex]

    [tex]= \sqrt{2.9*10^{9}} V/m[/tex]

    3. The attempt at a solution

    [tex]\Delta V = - E_{s}\Delta s[/tex]

    [tex]= -(\sqrt{2.9*10^{9}} V/m)(\frac{\sqrt{82}}{100} m)[/tex]

    [tex]= -4876.5 V[/tex]
     
  2. jcsd
  3. Mar 5, 2009 #2

    Delphi51

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    Homework Helper

    Don't you have to take the angle into account? Only a component of E is in the direction of the distance.
     
  4. Mar 5, 2009 #3

    LowlyPion

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    Homework Helper

    I think you take your

    ΔV = E*Δs a little differently. Namely as the dot product of the E vector and the s vector, such that

    ΔV = Ex*Δx i + Ey*Δy j
     
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