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Four point charges Q1, Q2, Q3, Q4, all of equal magnitude, are fixed on the x axis at x = -2a, -a, +a, +2a respectively. A positive test charge q is placed on the positive y axis at distance b > 0 from the origin. List-I gives four sign combinations; List-II gives possible directions of the net force on q. Match them. List-I: (P) all four positive; (Q) Q1, Q2 positive and Q3, Q4 negative; (R) Q1, Q4 positive and Q2, Q3 negative; (S) Q1, Q3 positive and Q2, Q4 negative. List-II: (1) +x; (2) -x; (3) +y; (4) -y.

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

Correct answer: P-3, Q-1, R-4, S-2

Solution

(P) All positive and symmetric about y axis: horizontal components cancel, all push q upward => +y => (3). (Q) Left pair (x<0) positive (repel, pushing q to +x and up), right pair negative (attract, pulling q toward them at +x and down); the symmetric arrangement makes the net horizontal component point +x; vertical components partly cancel leaving net +x => (1). (R) Q1(-2a) and Q4(+2a) positive, Q2(-a) and Q3(+a) negative: this is symmetric about the y axis so horizontal parts cancel; the inner negative charges (closer, attract downward) dominate over the outer positive (repel upward), net is downward => -y => (4). (S) Q1(-2a) positive, Q2(-a) negative, Q3(+a) positive, Q4(+2a) negative: not symmetric; working out the components the net force points in -x => (2). Matching: P-3, Q-1, R-4, S-2.

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