Question

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 ?

• A. +,-,+,-,-,+
• B. +,-,+,-,+,-
• C. +,+,-,+,-,-
• D. -,+,+,-,+,-

Answer 1

Answer: (D)

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