physics
posted by Natasha .
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?

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^23.6k/(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^23.6x^2=0
12.4x^2+106x+173)=0
x=(106+sqrt(106^24*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^217k/(x+3.2)^2=0
this changes the equation to
17x^2=3.6(x^2+6.4x+10.2)
13.4x^220.5x37=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.