Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4πε0)k, where k is :

The potential energy of a system of charges can be calculated using the formula U = k q1 q2 / r, where k = 1 / (4πε0), and r is the distance between the charges. When a third charge q3 is moved along an arc of a circle, the change in potential energy can be found by considering the initial and final positions of q3 relative to q1 and q2. The change in potential energy (ΔU) is given by ΔU = k q3 (q1 / r1 + q2 / r2), where r1 and r2 are the distances from q3 to q1 and q2, respectively. Given that q3 moves along an arc of a circle, the distances r1 and r2 change, but the question suggests a simplification where the change in potential energy is directly proportional to q3 and a constant k that depends on q1 or q2. Without explicit details on the initial and final positions or the exact path, we consider the general principle that the change in potential energy is proportional to the product of the charges and inversely proportional to the distance between them. The correct formula for k involves considering the geometry of the situation and how the distances between q3 and the other charges change as q3 moves along the arc.