Two charge q₁ and q₂ are placed 30 ~cm apart, as shown in the figure. A third charge q₃ is moved along the are of a circle of radius 40 ~cm from C to D . The change in the potential energy of the system is ( q₃ k 4 ₀ ), where k is:

Step-by-step solution

aligned & V_i= 1 4 ₀ [ q₁ q₃ (0.4) + q₁ q₂ (0.3) + q₂ q₃ (0.5) ] & v_f= 1 4 ₀ [ q₁ q₃ (0.4) + q₁ q₂ (0.3) + q₂ q₃ (0.1) ] aligned aligned & V=V f-V₁ & = 1 4 ₀ q₂ q₃ ( 1 0.1 - 1 0.5 ) & = q₂ q₃ ₀ (10⁻² )= q₃ 4 ₀ (8 q₂ ) & k=8 q₂ aligned