Four charges and of same magnitude are fixed along the -axis at and , respectively. A positive charge is placed on the positive -axis at a distance . Four options of the signs of these charges are given in List-I. The directions of the forces on the c

Question

Four charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ of same magnitude are fixed along the $x$ -axis at $x = - 2 a, - a, + a$ and $+ 2 a$ , respectively. A positive charge $q$ is placed on the positive $y$ -axis at a distance $b > 0$ . Four options of the signs of these charges are given in List-I. The directions of the forces on the charge $q$ is given in List-II. Match List-I with List-II and select the correct answer using the code given below the lists. [2014]

	List - I		List - II
P.	$Q_{1}, Q_{2}, Q_{3}, Q_{4}$ all positive	1.	$+ x$
Q.	$Q_{1}, Q_{2}$ positive; $Q_{3}, Q_{4}$ negative	2.	$- x$
R.	$Q_{1}, Q_{4}$ positive; $Q_{2}, Q_{3}$ negative	3.	$+ y$
S.	$Q_{1}, Q_{3}$ positive; $Q_{2}, Q_{4}$ negative	4.	$- y$

Codes:

	List - I		List - II
P.	$Q_{1}, Q_{2}, Q_{3}, Q_{4}$ all positive	1.	$+ x$
Q.	$Q_{1}, Q_{2}$ positive; $Q_{3}, Q_{4}$ negative	2.	$- x$
R.	$Q_{1}, Q_{4}$ positive; $Q_{2}, Q_{3}$ negative	3.	$+ y$
S.	$Q_{1}, Q_{3}$ positive; $Q_{2}, Q_{4}$ negative	4.	$- y$

Codes:

Smart Achievers · Accepted Answer

(1)

If $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ are all positive, then the force will be along $x = - 2 a, - a, + a$ -direction as components of forces along, the $x$ -axis cancel out each other.

If $Q_{1}, Q_{2}$ are positive and $Q_{3}, Q_{4}$ are negative, the force will act along $+ x$ -direction as components of forces along the $y$ -axis cancel out each other.

If $Q_{1}, Q_{4}$ are positive and $Q_{2}, Q_{3}$ are negative, then attractive force will dominate repulsive force and the force will be along $- y$ -direction.

If $Q_{1}, Q_{3}$ are positive and $Q_{2}, Q_{4}$ are negative, components of forces along the $y$ -axis cancel out each other. So net force on charge $q$ is along the $x$ -axis.

Solution

1 P-3, Q-1, R-4, S-2

2 P-4, Q-2, R-3, S-1

3 P-3, Q-1, R-2, S-4

4 P-4, Q-2, R-1, S-3

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