Two very large charged parallel metal plates are 10.0 cm apart and produce a uniform electric fi

step 1 In this question, we have two very large charged parallel metal plates that are 10 cm apart. And

Two very large charged parallel metal plates are 10.0 cm...

Two very large charged parallel metal plates are 10.0 $\mathrm{cm}$ apart and produce a uniform electric field of $2.80 \times 10^{6} \mathrm{N} / \mathrm{C}$ between them. A proton is fired perpendicular to these plates with an initial speed of 5.20 $\mathrm{km} / \mathrm{s}$ , starting at the middle of the negative plate and going toward the positive plate. How much work has the electric field done on this proton by the time it reaches the positive plate?

Key Concepts

Electric Field

An electric field is a region in space where a charged particle experiences a force, and its strength and direction are described by the field vector. In problems involving charged plates, the electric field is often uniform between the plates, meaning it has the same magnitude and direction at every point in that region.

Force on a Charged Particle

The force experienced by a charged particle in an electric field is given by F = qE, where q is the charge of the particle and E is the electric field. This force is responsible for accelerating the particle and doing work on it as it moves through the field.

Work and Energy in Electric Fields

Work in the context of electric fields is defined as the force acting on a charge multiplied by the displacement in the direction of the force. In a uniform electric field, the work done on a charged particle can be directly calculated as the product of the charge, the electric field strength, and the distance over which the force is applied. This work is related to the change in the particle's kinetic energy.

Electric Potential Difference

The electric potential difference, or voltage, between two points in an electric field is the work done per unit charge in moving a test charge between those points. In uniform fields, it is simply the product of the field strength and the separation distance, and it represents the energy change experienced by a charge moving across that distance.

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