Question

Two equal negative charges – q are fixed at points (o, a) and (o, – a). A positive charge Q is released from rest at the point (2a, o) on the X – axis. The charge Q will …… 

(A) move to the origin and remain at rest there 

(B) execute simple harmonic motion about the origin 

(C) move to infinity 

(D) execute oscillations but not simple harmonic motion

Answer 1

The correct option (D) execute oscillations but not simple harmonic motion

Explanation:

Force exerted by charges – q at A & B on charge Q are F₁ & F₂

F₁ = F₂ = [(KQq) / r²]

The resultant of F₁ & F₂ is equally inclined with X axis and is along

X – direction towards origin. Let resultant is F'

∴ (F')² = F² + F² + 2F²cosθ

= 2F² + 2F²­ cosθ

(F')² = 2F²(1 + cosθ)

as F ∝ (1/r²) hence F' ∝ (1/r²)

hence charge Q will move towards the origin & because of inertia it will overshoot origin o. Thus charge Q will oscillate about O but motion is not simple harmonic.