question_answer

A charge q is placed at the centre of the line joining two equal point charges each equal to Q. The system of 3 charges will be in equilibrium if q is equal to:

A)  \[+Q/4\]                            

B)  \[-Q/2\]

C)  \[+Q/2\]            

D)  \[-Q/4\]

Correct Answer: D

Solution :

For equilibrium of system of charges force produced between q and Q+ force produced between Q and \[Q=0\]                                 \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{qQ}{{{(r/2)}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{QQ}{{{r}^{2}}}=0\] \[\Rightarrow \]               \[\frac{4qQ}{{{r}^{2}}}+\frac{QQ}{{{r}^{2}}}=0\]                \[\Rightarrow \]               \[q=-\frac{Q}{4}\]