Physics Question on electrostatic potential and capacitance

Question

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 $\bigg(\frac{q_3}{4\pi\in_0}\bigg)k$ ,where k is:

wo charges q1 and q2 are placed 30 cm apart

Answer 1

Solution

u1 =14 $\pi\in_0$ [q1q2 30×10−2+q1q2 40×10-2+q2q3 50×10-2 ]
u2 =14 $\pi\in_0$ [q1q2 30×10−2+q1q3 40×10-2+q2q310×10-2 ]
Δu= u2−u1=q2q34 $\pi\in_0$ ×102[110−150]
=q2q34 $\pi\in_0$ ×450×100
=q34 $\pi\in_0$ (8q2)
∴k=8q2

Therefore, the correct option is (A): 8q2