Two large, parallel, metal plates carry opposite charges of...

Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by $45.0 \mathrm{mm},$ and the potential difference between them is 360 $\mathrm{V}$ . (a) What is the magnitude of the electric field (assumed to be uniform) in the region between the plates? (b) What is the magnitude of the force this field exerts on a particle with charge $+2.40 \mathrm{nC} ?$ (c) Use the results of part (b) to compute the work done by the field on the particle as it moves from the higher-potential plate to the lower. (d) Compare the result of part (c) to the change of potential energy of the same charge, computed from the electric potential.

Key Concepts

Uniform Electric Field

A uniform electric field is one that has the same magnitude and direction at every point. This condition is typically found between two parallel plates that are large compared to the separation between them, ensuring that edge effects can be neglected. In such fields, the force on a charged particle is constant, which simplifies calculations of motion and energy transfer.

Relation between Electric Potential Difference and Electric Field

The electric potential difference between two points in a uniform electric field is directly related to the field strength and the separation between those points through the relation V = Ed, where V is the potential difference, E is the electric field's magnitude, and d is the distance between the points. This concept allows us to determine the field magnitude when the potential difference and distance are known.

Force on a Charged Particle in an Electric Field

The force acting on a charged particle in an electric field is described by the equation F = qE, where q is the charge of the particle and E is the electric field strength. This force is responsible for the acceleration of the particle and is the fundamental principle behind the operation of many electronic and electrostatic devices.

Work Done by the Electric Field

The work done by an electric field on a charged particle as it moves through a potential difference is given by the equation W = qV, where V is the potential difference the particle moves through. This work is a measure of the energy transferred to or from the particle by the electric field, and it directly correlates with changes in the particle's electric potential energy.

Electric Potential Energy

Electric potential energy is the energy possessed by a charged particle due to its position in an electric field. Changes in this energy occur when the particle moves through different potentials, and the work done by or against the electric field is equal to the negative change in electric potential energy. This concept is central to understanding energy conservation in systems involving electric fields.

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