A charge +Q is uniformly distributed over a thin ring of the...

A charge $+Q$ is uniformly distributed over a thin ring of the radius $R$. The velocity of an electron at the moment when it passes through the centre $O$ of the ring, if the electron was initially at rest at a point $A$ which is very far always from the centre and on the axis of the ring is : (a) $\sqrt{\left(\frac{2 K Q e}{m R}\right)}$ (b) $\sqrt{\left(\frac{K Q e}{m}\right)}$ (c) $\sqrt{\left(\frac{K m e}{Q R}\right)}$ (d) $\sqrt{\left(\frac{K Q e}{m R}\right)}$

A charge $+Q$ is uniformly distributed over a thin ring of the radius $R$. The velocity of an electron at the moment when it passes through the centre $O$ of the ring, if the electron was initially at rest at a point $A$ which is very far always from the centre and on the axis of the ring is :
(a) $\sqrt{\left(\frac{2 K Q e}{m R}\right)}$
(b) $\sqrt{\left(\frac{K Q e}{m}\right)}$
(c) $\sqrt{\left(\frac{K m e}{Q R}\right)}$
(d) $\sqrt{\left(\frac{K Q e}{m R}\right)}$

Key Concepts

Conservation of Energy

This principle states that the total energy of a closed system remains constant. In electrostatics, when a charged particle moves in an electric field, its loss in potential energy is converted into kinetic energy. This concept is fundamental for determining the speed of a particle that starts from rest and moves under the influence of the electric field.

Conversion of Potential Energy to Kinetic Energy

Understanding how potential energy converts into kinetic energy is key when analyzing the motion of charged particles. The decrease in electric potential energy as a charge moves through the field results in an increase in its kinetic energy, allowing for the calculation of its velocity at different positions.

Electric Potential Due to a Charge Distribution

This concept involves calculating the electric potential created by a distribution of charge. In the context of a uniformly charged ring, the potential along the axis can be derived using integration, and it plays a crucial role in determining the energy landscape experienced by a test charge moving in the field.

Ring Geometry in Electrostatics

The geometry of a ring introduces symmetry that simplifies the calculation of the electric potential along its axis. This concept is important because the unique distribution affects how the potential decreases with distance, which is essential for analyzing the motion of charges influenced by the ring.

Coulomb's Constant and Coulomb's Law

Coulomb's constant appears in equations governing electric force and potential energy according to Coulomb's Law. This concept is crucial for quantifying the interactions between charges and is a fundamental part of calculating the forces and potential energies in electrostatic systems.

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