Two point charges of magnitude +3.00C and -5.00 C are placed along the x-axis at

Question

Two point charges of magnitude +3.00C and -5.00 C are placed along the x-axis at x=0 cm and x=40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net force because of the other two charges?

And can you explain the quadratic equation part and go step-by-step? That is the part that confuses me the most.

Explanation / Answer

Let us assume Two point charges of magnitudes +8.00 µC, and +10.0 µC are placed along the x-axis at x = 0 cm and x = 100? The E fields of the two charges are pointing in opposite directions between them. Therefore there is a point where the net E field = 0, where the two fields have equal magnitude but opposite directions 8/r1^2 = 10/r2^2 => r2^2 = 10*r1^2/4 =1.25r2^2 r1+r2 = 100 => r2 = 100-r1 => r2^2 = 10^4 - 200r1 + r1^2 1.25*r1^2 = 10^4 - 200r1 + r1^2 0.25*r1^2+200r1-10,000 = 0 Using the quadratic formula r1 = 47.2cm = 0.472m Substituting 0.472 into the equation does work. The equation should be 8uC/x^2 - 10uC/(1-x)^2 = 0 Not 8uC/x^2 - 10uC/1-x^2 = 0

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