Two point charges q ₁=6 C and q ₂=4 C are kept at points A and B in air where AB =10 ~cm . What is the increase in potential energy of the system when q ₂ is moved towards q ₁ by 2 cm ? ( 1 4 ₀ =9 10^9 SI units )

Step-by-step solution

The potential energy between two charges is given as U= K q₁ q₂ r Initial potential energy is U_i= K₁ q₂ r When charge q ₂ moves towards the q ₁ the separation between the charges becomes d - x The final potential energy is U_f= K₁ q₂ (d-x) The increase in potential energy is aligned & & U & =U_f-U_i & & U & = K q₁ q₂ (d-x) - K q₁ q₂ d =K q₁ q₂ ( 1 d-x - 1 d ) aligned U= Kq ₁ q ₂ x ~d ( ~d - x ) Substituting given values, array ll & U = (9 10^9 ) (6 10⁻⁶ ) (4 10⁻⁶ ) 0.02 (0.1)(0.1-0.02) & U= 4.32 10⁻³ 0.1 0.08 =0.5