JEE Advanced 2014 · Paper 2 · Physics Q17

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PhysicsList match+3 / -1Question 17 of 60

Four charges $Q_1$ , $Q_2$ , $Q_3$ and $Q_4$ of same magnitude are fixed along the $x$ axis at $x=-2a$ , $-a$ , $+a$ and $+2a$ , 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 direction 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.

Charges Q₁, Q₂, Q₃, Q₄ on the x-axis at (−2a, 0), (−a, 0), (+a, 0), (+2a, 0); charge q at (0, b) on the positive y-axis.

List I

P
$Q_1, Q_2, Q_3, Q_4$ all positive
Q
$Q_1, Q_2$ positive; $Q_3, Q_4$ negative
R
$Q_1, Q_4$ positive; $Q_2, Q_3$ negative
S
$Q_1, Q_3$ positive; $Q_2, Q_4$ negative

List II

1
$+x$
2
$-x$
3
$+y$
4
$-y$

P → 3; Q → 1; R → 4; S → 2

P → 4; Q → 2; R → 3; S → 1

P → 3; Q → 1; R → 2; S → 4

P → 4; Q → 2; R → 1; S → 3

Answer and worked solution

Official answer: A

Charges at $\pm a$ are the inner pair and those at $\pm2a$ the outer pair. A charge at $\pm a$ acts on $q$ more strongly than one at $\pm2a$ , and each pair is symmetric about the $y$ axis.

P (all positive): the $x$ components cancel; all push $q$ up. +y → 3.
Q ( $Q_1,Q_2$ positive, $Q_3,Q_4$ negative): the left charges push $q$ to the right and the right charges pull it to the right; the $y$ components cancel. +x → 1.
R ( $Q_1,Q_4$ positive, $Q_2,Q_3$ negative): symmetric, so the $x$ components cancel. The closer negative pair pulls down more than the outer positive pair pushes up. −y → 4.
S ( $Q_1,Q_3$ positive, $Q_2,Q_4$ negative): the $y$ components cancel in pairs ( $Q_1$ with $Q_4$ , $Q_2$ with $Q_3$ ). Along $x$ , the strong inner charges both act towards $-x$ ( $Q_3$ repels, $Q_2$ attracts), beating the weaker outer pair. −x → 2.

(A) P → 3, Q → 1, R → 4, S → 2

Topics:Coulomb's law and superposition

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JEE Advanced 2014 · Paper 2, Physics question 17