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Q.

Two fixed charges  4Q (positive) and -Q are located at  A and B respectively. The distance AB being 3m.

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a

If a negative charge is placed at P and displaced slightly along AB, it will execute oscillations

b

The point P where the resultant field due to both is zero is on AB inside AB

c

If a positive charge is placed at P and displaced slightly along AB, it will execute oscillations

d

The point P where the resultant field due to both is zero is on AB outside AB

answer is A, D.

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Detailed Solution

At any point to the left of charge 4Q,  electric field due to 4Q (leftwards) is stronger than that due to -Q(rightwards). Net electric field is towards left.

In-between the charges, fields due to both the charges is towards right. Net electric field is towards right.

Null point is possible only to the right of charge -Q.

Let null point P be at a distance of d to the right of charge -Q

K4Q3+d2=KQd2

d=3m

To the right of null point, net electric field will point towards right and to its left, net electric field will point towards left.

Hence a negative charge placed at null point will be in stable equilibrium along the line joining the charges. A positive charge will be in unstable equilibrium along the line joining the charges. 

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