A) \[-\frac{Q}{2}\]
B) \[-\frac{Q}{4}\]
C) \[+\frac{Q}{4}\]
D) \[+\frac{Q}{2}\]
Correct Answer: B
Solution :
Suppose in the following figure, equilibrium of charge B is considered. Hence for it's equilibrium \[|{{F}_{A}}|\,=\,|{{F}_{C}}|\] Þ \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{4{{x}^{2}}}=\]\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{qQ}{{{x}^{2}}}\] Þ \[q=\frac{-\,Q}{4}\] Short Trick: For such type of problem the magnitude of middle charge can be determined if either of the extreme charge is in equilibrium by using the following formula. If charge A is in equilibrium then q = ? \[{{Q}_{B}}\,{{\left( \frac{{{x}_{1}}}{x} \right)}^{2}}\] If charge B is in equilibrium then \[q=-{{Q}_{A}}\,\,{{\left( \frac{{{x}_{2}}}{x} \right)}^{2}}\] If the whole system is in equilibrium then use either of the above formula.You need to login to perform this action.
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