A charge q is placed at the centre of the line joining two equal charges

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electricfield

#1

A charge q is placed at the centre of the line joining two equal charges (Q). Show that the system of three charges will be in equilibrium,
q = - Q/4


#2

Suppose the three charges be placed as shown in the figure.

As, the net force on q is zero, so it is already in equilibrium. For equilibrium of other two charges-, the net force on each charge must be zero.