question_answer

Two unit negative charges are placed on a straight line. A positive charge q is placed exactly at the mid-point between these unit charges. If the system of three charges is in equilibrium the value of q (in C) is:

A)  1.0                                        

B)  0.75

C)  0.5                                        

D)  0.25

Correct Answer: D

Solution :

                 For equilibrium of charge q. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{-O\times q}{{{(r/2)}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(-Q)(-Q)}{{{r}^{2}}}=0\] \[\Rightarrow \]               \[4q=Q\] \[\Rightarrow \]               \[a=\frac{Q}{4}=\frac{1}{4}\]      \[(\because \,Q=1\,C)\]                 \[=0.25\,C\]