Two point charges +8 10⁻¹⁸ and +2 10⁻¹⁸ C are fixed 10 cm apart. Where should we place a third charge 10⁻⁷ C , so that it is in equilibrium?

Step-by-step solution

Since both charges are positive, the third charge must lie between them. Let x be the distance of the third charge from q₁ = +8 10⁻¹⁸ C, so its distance from q₂ = +2 10⁻¹⁸ C is (10 - x) cm. For equilibrium, forces from both charges must be equal: |q₁| x^2 = |q₂| (10-x)^2 8 10⁻¹⁸ x^2 = 2 10⁻¹⁸ (10-x)^2 4 x^2 = 1 (10-x)^2 Taking square root: 2 x = 1 10-x 2(10-x) = x 3x = 20 x 6.67 cm The third charge must be placed 6.67 cm from +8 10⁻¹⁸ C.