Question

A uniformly charged thin ring of linear charge density $+\lambda$ is shown in figure. An electron is placed on the ring's axis at a distance of $r$ from the centre of the ring and is constrained to stay on the axis of the ring. The motion of the electron when it is released from the rest is

• A. Along straight line and continuous to move toward +x axis.
• B. Oscillatory about O
• C. Along straight line and continuous to more toward - x axis
• D. The electron will remain stationary.

Answer 1

The correct option is B Oscillatory about O

The ring is positively charged, hence the electron will be attracted towards the centre $O$ of the ring. At $O$, net force is zero but on reaching $O$, the electron has some kinetic energy and due to inertia it crosses $O$. But on the other side it is further attracted towards $O$. Also since electric field due to positive charged ring is along the axis and away from the center, the force on the electron is towards the center.
Hence, motion of electron is oscillatory about $O$.