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Two charges, -17 and +3.6 µC, are fixed in place and separated by 3.2 m.
a) At what spot along a line through the charges is the net electric field zero? Locate this spot relative to the positive charge. (Hint: The spot does not necessarily lie between the two charges.
(b) What would be the force on a charge of +1 µC placed at this spot?

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    Between the charges, E is never zero, as it is in the same direction (towards the -17). To the left of the two charges, assuming the -17 is leftmost, one has E from the - charge to the right,and E from the + charge to the left. I suspect there wont be a zero there, lets check:

    Etotal=17k/x^2-3.6k/(3.2+x)^2=0?

    17(3.2^2+6.4x+x^2)=3.6x^2
    I am working this now approxiamtely, in my head, you do it accurately.
    173+106x+17x^2-3.6x^2=0
    12.4x^2+106x+173)=0
    x=(-106+-sqrt(106^2-4*12.4*173))/25
    x=about -4+-2.5
    but x has to be + in this model. No solution to the left.

    Now to the right of the 3.6microC, same idea

    E=3.6k/x^2-17k/(x+3.2)^2=0

    this changes the equation to
    17x^2=3.6(x^2+6.4x+10.2)
    13.4x^2-20.5x-37=0 appx
    x=(20.5+-sqrt(20.5^2+4*13.4*37)/26.8
    = 20.5/26.8 +-48/26.8
    = .76+- 1.79

    but x must be positive, so x=2.55m to the right of the positive charge. Of course, check it, I did it in my head.

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