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Resultant Electric field between charges

  1. Feb 27, 2017 #1
    1. The problem statement, all variables and given/known data
    A +15 microC point charge Q1 is at a distance of 20 mm from a + 10 microC charge Q2.
    Fin the resultant electric field at:
    Ai) the midpoint between the two charges
    ii) at point P along the line between Q1 and Q2 which is 25 mm from Q1 and 45 mm from Q2.
    bi) Explain why there is a point along the line between the two charges at which the electric field is zero
    ii) Calculate the distance from this point to Q1 and to Q2
    2. Relevant equations
    I know the eleectric field can be calculated using E = (kQ)/r^2 but I am unsure how to calculate this.

    3. The attempt at a solution
    The answers at the back of the book say the answers are:
    ai) 4.5 x 10^8 V/m towards Q2
    ii) 2.6 x 10^ V/m away from Q1
    bii) 11 mm from Q1, 9 mm from Q2


    But I cant seem to get these answers.
     
  2. jcsd
  3. Feb 27, 2017 #2

    gneill

    User Avatar

    Staff: Mentor

    Show us what you've tried, even if you haven't obtained the book's answers. No help can be offered until you show your work.
     
  4. Feb 28, 2017 #3
    For ai)
    E1 = kq/d^2 = ([8.9 x10^9] x [15 x 10^-6])/(10x10^-3)^2 = 1.335 x10^ 9 V/m
    E2 = kq/d^2 = ([8.9 x10^9] x [1o x 10^-6])/(10x10^-3)^2 = 8.9 x10^ 9 V/m
    Enet = E1 - E2 = 4.45 x 10^8 V/m towards Q2

    aii)
    E1 = kq/d^2 = ([8.9 x10^9] x [15 x 10^-6])/(25x10^-3)^2 = 2.14 x10^8 V/m
    E2 = kq/d^2 = ([8.9 x10^9] x [10 x 10^-6])/(45x10^-3)^2 = 4.4 x10^7 V/m
    Enet = E1 - E2 = 1.7 x 10^8 V/m away from Q1

    bi) Is this the idea that due to the forces having the same magnitude, but in opposite directions, the electric field is zero.
    bii) I am unsure of how to do this one.
     
  5. Feb 28, 2017 #4

    gneill

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    Staff: Mentor

    Looks good so far!
    You'll need to write an equation for the electric field at any point along a line between the two charges. How might you specify such a point? Start with a drawing of the setup.
     
  6. Feb 28, 2017 #5
    This is one that I am really unsure of
     
  7. Feb 28, 2017 #6
    Electric field can be zero only and only ##\vec E_{total}=0##.So

    ##\vec E_{1}+\vec E_{2}=0##

    Their magnitudes must be be same in this case.Logically think in which point Electric field could be 0.Deterime the distances and use the upper equation.
     
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