A uniform electric field of magnitude 327 N / C is directed along the +y -axis. A 5.40-μC charg

step 1 this question we have a charge of 5 .40 microculum. It is placed at the origin and then in this

A uniform electric field of magnitude 327 N / C is directed...

A uniform electric field of magnitude $327 \mathrm{~N} / \mathrm{C}$ is directed along the $+y$ -axis. A $5.40-\mu \mathrm{C}$ charge moves from the origin to the point $(x, y)=(-15.0 \mathrm{~cm},-32.0 \mathrm{~cm})$. (a) What is the change in the potential energy associated with this charge? (b) Through what potential difference did the charge move?

Key Concepts

Work-Energy Principle in Electrostatics

In electrostatics, the work done by the electric field on a charge is directly related to the change in the electric potential energy of the charge. By applying the work-energy principle, one can understand that the work done moving a charge in a conservative electric field is equal to the negative change in its electric potential energy, linking the dynamics of the charge to its energy configuration.

Electric Potential Energy

Electric potential energy is the energy that a charge possesses by virtue of its position in an electric field. The change in electric potential energy, which can be determined by multiplying the charge by the change in electric potential, reflects the work done on or by the charge as it moves in the field.

Uniform Electric Field

A uniform electric field is one in which the strength and direction of the field remain constant throughout the region of interest. This concept is essential because it simplifies calculations by ensuring that the force on a charge remains constant, which directly affects both work done and potential energy changes when a charged particle is moved within the field.

Electric Potential Difference

The electric potential difference between two points is defined as the work done per unit charge by the electric field when moving a charge between those points. This concept is crucial for understanding energy changes in the system, especially in a uniform field where the difference can be calculated directly from the product of the field strength and the component of displacement along the field direction.

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