Two point charges +10 C and 4 C are placed 10 cm apart in air. The work required to be done to bring them 2 cm closer is ( 1 4 ₀ =9 10^9 SI units )

Step-by-step solution

The work done to bring two point charges closer equals the change in their electrostatic potential energy. The potential energy U for point charges q₁ and q₂ separated by distance r is U = 1 4 ₀ q₁ q₂ r . Given q₁ = +10 C = 10 10⁻⁶ C , q₂ = +4 C = 4 10⁻⁶ C , with 1 4 ₀ = 9 10^9 N m^2/C^2 . Initial separation r₁ = 0.10 m , final separation r₂ = 0.08 m after moving 2 cm closer. The work W equals the difference in potential energy: W = U₂ - U₁ . Using U = k q₁ q₂ r with k = 9 10^9 : U₁ = (9 10^9)(10 10⁻⁶)(4 10⁻⁶) 0.10