Question

Two fixed charges 4Q (positive) and Q (negative) are located at A and B, the distance AB being 3 m -

• A. The point P where the resultant field due to both is zero is on AB outside AB.
• 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. If a negative charge is placed at P and displaced slightly along AB it will execute oscillations.

Answer 1

Answer: (A), (D)

A, D

Answer 2

The point where the electric field is zero due to two charges of opposite sign lies on the line joining the charges, outside the region between the charges, and closer to the charge with the smaller magnitude. In this case, $|-Q| < |+4Q|$, so the zero field point is outside AB and closer to B. Calculation shows this point is at $x=6$ m, which is on the line AB outside AB. Thus, option (A) is correct and (B) is incorrect.

For a charge placed at an equilibrium point, the equilibrium is stable if a small displacement results in a restoring force, and unstable if it results in a force away from the equilibrium. We found that for a positive charge, displacement along AB results in a force away from P, so the equilibrium is unstable. For a negative charge, displacement along AB results in a force towards P, so the equilibrium is stable and the charge will execute oscillations. Thus, option (C) is incorrect and (D) is correct.