Two point charges of 12ûC and …

We can use the formula for electrostatic potential energy to calculate the work done in bringing the two point charges closer. The formula for electrostatic potential energy is: U = k*q1*q2/r where U is the electrostatic potential energy, k is Coulomb's constant (= 9 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges in Coulombs, and r is the distance between the charges in meters. Initially, the charges are 10 cm = 0.1 m apart, so the initial distance r1 is 0.1 m. The final distance r2 when the charges are 4 cm = 0.04m apart. The magnitudes of the charges are q1 = 12 uC = 12 x 10^-6 C, and q2 = 8 uC = 8 x 10^-6 C. Using the formula and plugging in the values, we get: U1 = k*q1*q2/r1 = (9 x 10^9 Nm^2/C^2)(12 x 10^-6 C)(8 x 10^-6 C)/(0.1 m) ≈ 8.64 x 10^-5 J U2 = k*q1*q2/r2 = (9 x 10^9 Nm^2/C^2)(12 x 10^-6 C)(8 x 10^-6 C)/(0.04 m) ≈ 3.456 x 10^-4 J The change in electric potential energy ΔU is U2 - U1 = 2.594 x 10^-4 J. Therefore, the work done in bringing the charges 4cm closer is 2.594 x 10^-4 Joules.