Question

A +4.00 μC point charge and -6.00 μC point charge are placed along the x-axis at x = 0.000 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 electric force due to the other two charges?

A) -1.78 m

B) 1.78 m

C) 0.180 m

D) -0.200 m

E) -0.180 m

Answer 1

Since 4uC is smaller in magnitude, the third charge has to be placed in left of it.

Now, by coloumbs law,

k*4e-6q/r^2 - k*6e-6q/(0.4+r)^2 = 0

4/r^2 = 6/(0.4+r)^2

6r^2 = 4*(0.4+r)^2

  6r^2 = 4*(r^2+0.8r + 0.16)

2r^2 -3.2 r - 0.64 = 0

r = 1.78 m on left

hence it is -1.78m

option A