Two point charges +e and +4e are kept at a distance 'd' units apart. Third point charge +q is placed between the two charges at a distance 'x' units from charge +e so as to be in equilibrium. The value of 'x' is

Step-by-step solution

Let the charges +e and +4e be placed at a distance d apart. The third charge +q is placed at a distance x from +e . The distance of +q from +4e is (d - x) . For the charge +q to be in equilibrium, the net force acting on it must be zero. The force exerted by +e must be equal in magnitude and opposite in direction to the force exerted by +4e . 1 4 ₀ e q x^2 = 1 4 ₀ 4e q (d - x)^2 1 x^2 = 4 (d - x)^2 Taking the square root on both sides: 1 x = 2 d - x d - x = 2x 3x = d x = d 3 Answer: d 3 units