A proton is released from rest at the positive plate of a...

A proton is released from rest at the positive plate of a parallel-plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of $50,000 \mathrm{m} / \mathrm{s}$. The experiment is repeated with a He $^{+}$ ion (charge $e$, mass 4 u). What is the ion's speed at the negative plate?

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Key Concepts

Uniform Electric Field

A uniform electric field is one in which the field strength and direction remain constant over a given region. In the context of a parallel-plate capacitor, this uniform field creates consistent forces on charged particles, leading to uniform acceleration as the particle moves from one plate to the other.

Energy Conservation in Electrostatics

When a charged particle moves through a potential difference, the work done by the electric field is converted into kinetic energy. This principle of energy conservation is used to relate the potential difference experienced by the particle to its increase in kinetic energy, allowing for the calculation of its final speed.

Dependence of Final Velocity on Mass and Charge

The final speed of a charged particle accelerated by an electric field is determined by the ratio of its charge to its mass. According to the equation v = ?(2q?V/m), particles with a smaller mass or larger charge will achieve higher speeds for the same potential difference. This relationship is crucial in comparing the accelerations of different particles under identical conditions.

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