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 ?

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 ?

(a) \( 8q_1 \)

(b) \( 6q_1 \)

(c) \( 8q_2 \)

(d) \( 6q_2 \)

Answer :  (c) \( 8q_2 \)

\( V = \frac{U_{\text{(scalar) }}}{q} \)

\( \vec{E} = \frac{F_{\text{(vector) }}}{q} \)

\( \Delta U = U_D - U_C \)

\( U_D = k \frac{q_1 q_3}{\frac{40}{100}} + k \frac{q_2 q_3}{\frac{10}{100}} \)

\( U_C = k \frac{q_1 q_3}{\frac{40}{100}} + k \frac{q_2 q_3}{\frac{50}{100}} \)

\( \Delta U = k q_2 q_3 \cdot 100 \left[ \frac{1}{10} - \frac{1}{50} \right] \)

\( \quad = k q_2 q_3 \cdot 100 \cdot \frac{5 - 1}{50} \)

\( \quad = k q_2 q_3 \cdot 8 \)