question_answer

Two point charges \[+9e\] and \[+e\] are at 16 cm away from each other. Where should another charge q be placed between them so that the system remains in equilibrium [MP PET 2002]

A)            24 cm from \[+9e\]           

B)            12 cm from \[+9e\]

C)            24 cm from \[+e\]              

D)            12 cm from \[+e\]

Correct Answer: B

Solution :

                     Suppose q is placed at a distance x from +9e, then for equilibrium net force on it must be zero i.e. \[\left| {{F}_{1}} \right|\text{ }=\text{ }\left| {{F}_{2}} \right|\] Which gives \[{{x}_{1}}=\frac{x}{\sqrt{\frac{{{Q}_{2}}}{{{Q}_{1}}}}+1}=\frac{16}{\sqrt{\frac{e}{9e}}+1}=12\,cm\]