question_answer

Two charges \[4q\] and \[q\] are placed at distance\[l\]. In the middle adjoining line a charge\[Q\]is kept. If resultant force on \[q\] will be zero, then \[Q\] will be

A)  \[+q\]           

B)  \[-q\]

C)  \[+2q\]           

D)  \[-2g\]

Correct Answer: B

Solution :

 Here \[{{F}_{AB}}+{{F}_{CB}}=0\] \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{4{{q}^{2}}}{{{l}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Qq}{{{l}^{2}}/4}=0\] \[\Rightarrow \] \[4Qq=-4{{q}^{2}}\] \[\Rightarrow \] \[Q=-q\]