What potential difference between the two plates would be...

What potential difference between the two plates would be needed to accelerate a hydrogen ion (a proton) from rest to a speed of $10^6 \mathrm{~m} / \mathrm{s}$ ?
(A) $100 \mathrm{~V}$
(B) $500 \mathrm{~V}$
(C) $1000 \mathrm{~V}$
(D) $5000 \mathrm{~V}$
(E) $10,000 \mathrm{~V}$

Key Concepts

Kinetic Energy Equation

The kinetic energy formula, ½ mv², quantifies the energy a particle possesses as a result of its motion. It is a key concept when analyzing how much energy a particle gains upon acceleration and forms a fundamental aspect of relating the physical quantities involved in particle dynamics.

Conservation of Energy

This principle states that energy cannot be created or destroyed, only converted from one form to another. In the context of particle acceleration, the electric potential energy provided by a voltage difference is entirely converted into the kinetic energy of the particle, allowing one to relate the work done by the electric field to the particle's speed.

Electric Potential Difference

Electric potential difference, measured in volts, represents the work done per unit charge to move a charge between two points in an electric field. It is the source of the energy that accelerates charged particles and is directly related to the kinetic energy gained by a particle as it moves through the potential difference.

Energy Conversion in Particle Acceleration

When a charged particle is accelerated by an electric field, the work done by the field on the charge is converted into the particle's kinetic energy. The equation qV = ½ mv² encapsulates this conversion, linking the potential difference to the particle's mass, charge, and velocity.

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