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બે સમાન બિંદુવત વિદ્યુતભાર $q$ ને જોડતી રેખાના મધ્યબિંદુએ એક વિદ્યુતભાર $Q$ ને મૂકેલ છે. $q$ ના કયા મૂલ્ય માટે આ તંત્ર સમતુલનમાં હશે?
$-Q/3$
$-Q/4$
$Q/2$
$-Q/2$
Solution
Step $1:$ Equilibrium of central charge $Q$ [Ref. Fig. $1$]
For the system to be in equilibrium net force on each charge should be zero.
By Symmetry, both outer charges $q$ will exert equal and opposite force on $Q$, which will cancel out. As shown in Figure $1$.
Hence Net force on $Q$ will always be zero irrespective of value of charge.
Step $2:$ Equilibrium of outer charge $q$ [Ref. Fig. $2]$
Net force on charge $q$ at the right, due to other two charges should be zero.
$F_q=\frac{K Q q}{x^2}+\frac{K^2}{(2 x)^2}=0$
$\Rightarrow \frac{K Q q}{x^2}=-\frac{K^2}{4 x^2}$
$\Rightarrow Q=\frac{-q}{4}$
