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  4. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R Which of the following arrangements of charge is possible for, P, Q, R, S, T and U respectively ?

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Q. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of same magnitude is placed at $R$ Which of the following arrangements of charge is possible for, $P, Q, R, S, T$ and $U$ respectively ?Physics Question Image

IIT JEEIIT JEE 2004Electrostatic Potential and Capacitance

Solution:

According to option $(d)$ the electric field due to $P$ and $S$ and due to $Q$ and $T$ add to zero.
While due to $U$ and $R$ will be added up. Hence, the correct option is $(d)$.
$(P)$ Component of forces along $x$-axis will vanish.
Net force along positive $7$-axis
$E_3 < E_1 < E_2 $
$(Q)$ Component of forces along $7$-axis will vanish.
Net force along positive $x$-axis
$(R)$ Component of forces along $x$-axis will vanish.
Net force along negative $7$-axis
$(S)$ Component of forces along $7$-axis will vanish.
Net force along negative $x$-axis

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