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 change in potential energy of the system when $q_3$ is moved from C to D can be calculated by considering the work done against the electric field due to $q_1$ and $q_2$. However, without specific details on the initial and final positions (C and D) relative to $q_1$ and $q_2$, we can consider a general approach. The potential energy of a system of charges is given by $U=\frac{1}{4\pi {ϵ}_0}{\sum }_{i<j}\frac{q_i{q}_j}{r_{ij}}$. When $q_3$ moves, the distances $r_{13}$ and $r_{23}$ change, affecting the potential energy. The change in potential energy $\Delta U$ can be related to the initial and final configurations. If we consider $q_3$ moving in a way that its distance to $q_1$ and $q_2$ changes, the exact change in potential energy depends on these distances and the charges $q_1$ and $q_2$. The formula provided in the question, $\Delta U=\frac{q_3}{4\pi {ϵ}_0}k$, implies that $k$ represents the change in the potential due to $q_1$ and $q_2$ as $q_3$ moves. Without the exact geometry or how $q_3$ moves relative to $q_1$ and $q_2$, we cannot directly calculate $k$. However, the question suggests a relationship between the change in potential energy and the charges, which typically involves the product of charges and the inverse of the distance between them.