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Two charges q1 = + 2 μC and q2 = + 6 μC are 15.0 m apart. What is the distance from charge q1 to the point on the line segment joining the two charges where the electric field is zero?

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Answer 1

We can drop the “micro-coulomb” without any change in the problem. So we have, using Coulomb’s law:

2/r^2 + -6/(15-r)^2 = 0 , valid only for 0 < r < 15

2/r^2 = 6/(15-r)^2

2*(15-r)^2 = 6*r^2

2*(r^2–30r+225) = 6*r^2

r^2–30r+225 = 3*r^2

2r^2+30r-225 = 0

Apply the quadratic formula:

r = (-30 +/- sqrt(30^2 + 4*2*225))/(2*2)

r = (-30 +/- sqrt(2700))/4

r = (-30 +/- 30*sqrt(3))/4

r = (15/2)*(-1 +/- sqrt(3)) , valid only for 0 < r < 15

r = (15/2)*(-1 + sqrt(3)) ~= 5.49 (which is in the valid region)

r ~= 5.49