Electrostatics Question 753
Question: Two charges $ q _{1} $ and $ q _{2} $ are placed 30 cm apart. 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\pi {\in _{0}}}k, $ where k is
Options:
A) $ 8q _{1} $
B) $ 6q _{1} $
C) $ 8q _{2} $
D) $ 6q _{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] We know that potential energy of discrete system of charges is given by
$ U=\frac{1}{4\pi {\varepsilon _{0}}}( \frac{q _{1}q _{2}}{r _{12}}+\frac{q _{2}q _{3}}{r _{23}}+\frac{q _{3}q _{1}}{r _{31}} ) $
According to question, $ {U _{initial}}=\frac{1}{4\pi {\varepsilon _{0}}}( \frac{q _{1}q _{2}}{0.3}+\frac{q _{2}q _{3}}{0.5}+\frac{q _{3}q _{1}}{0.4} ) $
$ {U _{\text{final}}}=\frac{1}{4\pi {\varepsilon _{0}}}( \frac{q _{1}q _{2}}{0.3}+\frac{q _{2}q _{3}}{0.1}+\frac{q _{3}q _{1}}{0.4} ) $
$ {U _{initial}}-{U _{\text{final}}}=\frac{1}{4\pi {\varepsilon _{0}}}( \frac{q _{1}q _{2}}{0.3}-\frac{q _{2}q _{3}}{0.5} ) $
$ =\frac{1}{4\pi {\varepsilon _{0}}}[ 10q _{2}q _{3}-2q _{2}q _{3} ]=\frac{q _{3}}{4\pi {\varepsilon _{0}}}( 8q _{2} ) $
