question_answer

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 \[\frac{{{q}_{3}}}{4\pi {{\varepsilon }_{0}}}k,\] where k is

A)  \[8{{q}_{2}}\]

B)  \[8{{q}_{1}}\]

C)  \[6{{q}_{2}}\]

D)  \[6{{q}_{1}}\]

Correct Answer: A

Solution :

Change in potential energy\[(\Delta U)={{U}_{f}}-{{U}_{i}}\] \[\Rightarrow \]\[\Delta U=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \left( \frac{{{q}_{1}}{{q}_{3}}}{0.4}+\frac{{{q}_{2}}{{q}_{3}}}{0.1} \right)-\left( \frac{{{q}_{1}}{{q}_{3}}}{0.4}+\frac{{{q}_{2}}{{q}_{3}}}{0.5} \right) \right]\] \[\Rightarrow \]\[\Delta U=\frac{1}{4\pi {{\varepsilon }_{0}}}[8{{q}_{2}}{{q}_{3}}]=\frac{{{q}_{3}}}{4\pi {{\varepsilon }_{0}}}(8{{q}_{2}})\] \[\Rightarrow \] \[k=8{{q}_{2}}\]