Two charges q1 and q2 are placed 30 cm apart as shown in the figure. A third cha

Question

Two charges

q_{1}

and

q_{2}

are placed 30 cm apart as shown in the figure. A third charge

q_{3}

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

\frac{q_{3}}{4 π ϵ_{0}} k

, where k is

Options:

A . 8q2

B . 8q1

C . 6q2

D . 6q1

Answer: Option A
:
A

Change in potential energy

(Δ U) = U_{f} - U_{i}

\Rightarrow Δ U = \frac{1}{4 π ϵ_{0}} [(\frac{q_{1} q_{3}}{0.4} + \frac{q_{2} q_{3}}{0.1}) - (\frac{q_{1} q_{3}}{0.4} + \frac{q_{2} q_{3}}{0.5})]

\Rightarrow Δ U = \frac{1}{4 π ϵ_{0}} [8 q_{2} q_{3}] = \frac{q_{3}}{4 π ϵ_{0}} (8 q_{2})

∴ k = 8 q_{2}

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