Two charges each of charge +10 C are kept on Y -axis at y=-a and y=+a , respectively. Another point charge -20 C is placed at the origin and given a small displacement x(x< < a) along X -axis. The force acting on the point charge is (x and a are in metres, 1 4 ₀ =9 10^9 ~N - m ^2 C ⁻² )

Step-by-step solution

If force acting on each charge +10 C be F and x be the displaced position aligned & Net force F _ net = F + F & =2 ~F aligned From coulomb's law, aligned & k= 1 4 ₀ =9 10^9 Nm ^2 / C ^2 & F=9 10^9 10 10⁻⁶ 20 10⁻⁶ ( a^2+x^2 )^2 & =9 10^9 200 10⁻¹² (a^2+x^2 ) & F _ net =2 ~F =2 10 10^9 200 10⁻¹² (a^2+x^2 ) & F _ net =2 9 2 10⁻¹ (a^2+x^2 ) ( x a^2+x^2 ) & ( = x a^2+x^2 ) & =36 10⁻¹ x (a^2+x^2 )^ 3 / 2 aligned Given, x< < a so, neglecting x^2 F _ net =36 x (a^2 )^ 3 / 2 36 x a^3 ~N