Two point charges q₁ = 6 C and q₂ = 4 C are kept at points A and B in air where distance AB = 10 cm. What is the increase in potential energy of the system when q₂ is moved towards q₁ , by 2 cm ? ( 1 4 ₀ = 9 10^9 SI units )

Step-by-step solution

Initial potential energy of the system is given by U_i = 1 4 ₀ q₁ q₂ r_i Final potential energy of the system is given by U_f = 1 4 ₀ q₁ q₂ r_f Increase in potential energy U = U_f - U_i = q₁ q₂ 4 ₀ ( 1 r_f - 1 r_i ) Substituting the given values: q₁ = 6 10⁻⁶ C q₂ = 4 10⁻⁶ C r_i = 10 cm = 0.1 m r_f = 10 - 2 = 8 cm = 0.08 m U = 9 10^9 6 10⁻⁶ 4 10⁻⁶ ( 1 0.08 - 1 0.1 ) U = 216 10⁻³ (12.5 - 10) U = 0.216 2.5 = 0.54 J Answer: 0.54 J