Electrostatics 1 Question 8
8. 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?
(2004, 1M)
(a) + , - , + , - , - , +
(b) + , - , + , - , + , -
(c) + , + , - , + , - , -
(d) - , + , + , - , + , -
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Answer:
Correct Answer: 8. (d)
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 $y$-axis
(Q) Component of forces along $y$-axis will vanish. Net force along positive $x$-axis
(R) Component of forces along $x$-axis will vanish. Net force along negative $y$-axis
(S) Component of forces along $y$-axis will vanish. Net force along negative $x$-axis
