A particle with charge $+4.20$ nC is in a uniform electric field $E$ directed to the left. The charge is released from rest and moves to the left; after it has moved $6.00$ cm, its kinetic energy is $+2.20x{10}^{-6}$ J. What is the work done by the electric force?

Verified step by step guidance

1. Understand that the work done by the electric force on the particle is equal to the change in kinetic energy of the particle. This is based on the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
2. Identify the initial kinetic energy of the particle. Since the particle is released from rest, its initial kinetic energy is 0 J.
3. Calculate the change in kinetic energy. The final kinetic energy is given as 2.20 × 10^-6 J, and the initial kinetic energy is 0 J. Therefore, the change in kinetic energy is 2.20 × 10^-6 J - 0 J = 2.20 × 10^-6 J.
4. Recognize that the work done by the electric force is equal to the change in kinetic energy, which is 2.20 × 10^-6 J. This is because the work-energy principle states that the work done by forces on an object is equal to the change in its kinetic energy.
5. Conclude that the work done by the electric force on the particle as it moves 6.00 cm to the left is 2.20 × 10^-6 J.

Key Concepts

Electric Field

An electric field is a region around a charged particle where a force would be exerted on other charges. It is represented by the vector E and is measured in newtons per coulomb (N/C). The direction of the electric field is defined as the direction a positive test charge would move if placed in the field.

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this context, the work done by the electric force on the charged particle is equal to the increase in its kinetic energy as it moves through the electric field.

Electric Force

Electric force is the force exerted by an electric field on a charged particle. It is calculated using the formula F = qE, where q is the charge and E is the electric field strength. This force causes the particle to accelerate, changing its kinetic energy as it moves through the field.