A particle with charge +7.60 nC is in a uniform electric field directed to the left. Another for

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A particle with charge +7.60 nC is in a uniform electric...

A particle with charge $+7.60 \mathrm{nC}$ is in a uniform electric field directed to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest, it moves to the right. After it has moved 8.00 $\mathrm{cm}$ , the additional force has done $6.50 \times 10^{-5} \mathrm{J}$ of work and the particle has $4.35 \times 10^{-5} \mathrm{J}$ of kinetic energy. (a) What work was done by the electric force? (b) What is the potential of the starting point with respect to the end point? (c) What is the magnitude of the electric field?

Key Concepts

Work-Energy Theorem

This principle states that the work done on an object by all forces equals the change in the object's kinetic energy. It underpins the analysis of energy changes in a system, allowing us to link the work done by various forces to the observed changes in speed or motion.

Electric Force on a Charged Particle

A charged particle in an electric field experiences a force equal to the product of its charge and the electric field strength. The work done by this force when the particle moves through the field is directly related to changes in the particle’s potential energy.

Electric Potential Difference

This concept describes the difference in electric potential (voltage) between two points, representing the work per unit charge required to move a particle between those points. It is crucial for understanding how energy is transferred in electric fields as a charge moves.

Uniform Electric Fields

In a uniform electric field, the field strength and direction remain constant throughout the region. This property simplifies the relationship between the field, the work done by the field, and the potential difference over a given distance, often expressed as E = V/d.

Superposition of Forces and Work Contributions

When multiple forces act on a particle simultaneously, the total work is the sum of the work done by each force. This concept is important in problems where non-electric forces contribute to the motion, necessitating the separation and analysis of individual work contributions to determine the net energy change.

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