Two spheres of electric charges ( +2 nC ) and ( -8 nC ) are placed at a distance ' ( d ) ' apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

Step-by-step solution

Given, two charges ( +2 nC ) and ( -8 nC ) are placed distance ( d ) apart. Therefore, [ |F|= 1 4 ₀ (2 10⁻⁹ ) (8 10⁻⁹ ) d² = k (16 10⁻¹⁸ ) d² ] When the charges are joined together, then [ |F^ |= 1 4 ₀ 9 10⁻¹⁸ d¹² = k (9 10⁻¹⁸ ) d¹² ] Now, [ array l |F|= |F^ | k (16 10⁻¹⁸ ) d² = k (9 10⁻¹⁸ ) d¹² 16 d² = 9 d¹² d¹²= 9 16 d² d¹= 3 4 d array ] Therefore, in order to have same repulsive force as before the new distance between them should be ( 3 4 d )