# Two equal negative charges – q are fixed at points (0,-a) and (0,a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will (A) Execute simple harmonic motion about the origin (B) Move to the origin and remain at rest (C) Move to infinity (D) Execute oscillatory but not simple harmonic motion

The correct answer is (D) Execute oscillatory but not simple harmonic motion

### Solution

Motion is simple harmonic only if the charge Q is released from a point not very far from the origin on the x-axis.

Else where, motion is periodic but not simple harmonic.

#### The motion of Charged Particle in Electric Field

If a charged particle of charge Q is placed in an electric field of strength E, the force experienced by the charged particle = EQ.

• The acceleration of the charged particle in the electric field, a = EQ/m.
• The velocity of the charged particle after time t is = (EQ/m)t if the initial velocity is zero.
• The distance travelled by the charged particle is S = (1/2) × at2 = 1/2(EQ/m) × t2 if the initial velocity is zero.
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