A) \[8{{q}_{1}}\]
B) \[6{{q}_{1}}\]
C) \[8{{q}_{2}}\]
D) \[6{{q}_{2}}\]
Correct Answer: C
Solution :
[c] We know that potential energy of discrete system of charges is given by \[U=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{{{q}_{1}}{{q}_{2}}}{{{r}_{12}}}+\frac{{{q}_{2}}{{q}_{3}}}{{{r}_{23}}}+\frac{{{q}_{3}}{{q}_{1}}}{{{r}_{31}}} \right)\] According to question, \[{{U}_{\operatorname{initial}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{{{q}_{1}}{{q}_{2}}}{0.3}+\frac{{{q}_{2}}{{q}_{3}}}{0.5}+\frac{{{q}_{3}}{{q}_{1}}}{0.4} \right)\] \[{{U}_{\text{final}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{{{q}_{1}}{{q}_{2}}}{0.3}+\frac{{{q}_{2}}{{q}_{3}}}{0.1}+\frac{{{q}_{3}}{{q}_{1}}}{0.4} \right)\] \[{{U}_{\operatorname{initial}}}-{{U}_{\text{final}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{{{q}_{1}}{{q}_{2}}}{0.3}-\frac{{{q}_{2}}{{q}_{3}}}{0.5} \right)\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ 10{{q}_{2}}{{q}_{3}}-2{{q}_{2}}{{q}_{3}} \right]=\frac{{{q}_{3}}}{4\pi {{\varepsilon }_{0}}}\left( 8{{q}_{2}} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
