Two charged particles each having charge ' q ' and mass ' m ' are held at rest while their separation is ' r '. The speed of the particles when their separation is ' r 2 , will be ( ₀= permittivity of the medium)

Step-by-step solution

By conservation of energy for the system of two charges, ( K.E. + P.E. )_ initial =( K.E. + P.E. )_ final Initially the charges are at rest, KE _ initial =0 , Final K.E. =- 1 2 (2 ~m ) v ^2 ...(Like charges repel each other) array ll & (0+ ( 1 4 ₀ q^2 r ) )= (- 1 2 (2 m) v^2+ ( 1 4 ₀ q^2 r / 2 ) ) & ( 1 4 ₀ q^2 r )= (-m v^2+ ( 1 4 ₀ q^2 r / 2 ) ) & m v^2= q^2 4 ₀ ( 2 r - 1 r ) & v= q 4 m r array