Two small conducting balls of identical mass 20 ~g and identical charge 10⁻¹⁰ C hang from non-conducting threads of length, L=300 ~cm . If the equilibrium separation of balls is x and x L then the magnitude of x is (Assume, 4 ₀= 1 9 10^9 ~F / m and g=10 ~m / s ^2 )

Step-by-step solution

Given, mass of each spherical ball, m=20 ~g =2 10⁻² ~kg , g=10 ~m / s ^2 charge on each spherical ball, q₁=q₂=q=10⁻¹⁰ C and length of thread, L=300 ~cm =3 ~m According to the question, Equilibrium at point B , aligned T & =m g T & =F T & = 1 4 ₀ q^2 x^2 aligned (From Coulomb's law) From Eqn. (i) and (ii), we get T T = 1 4 ₀ q^2 x^2 m g [ Given, 4 ₀= 1 9 10^9 C ^2 / N - m ^2 ] m g =9 10^9 q^2 x^2 From A B M , = x 2 L^2- ( x 2 )^2 = x 4 L^2-x^2 = x 2 L ( L>x) From Eq. (iii), we get m g x 2 L = 9 10^9 q^2 x^2 Putting