Question

The distance between two charges q1= 4*10^-6C and q2 = 8 *10^-6C is 15.0 cm. Calculate the distance from charge q, to the points on the line
segment joining the two charges where the electric field is zero​

Answer 1

Answer: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

Explanation: