91Ó°ÊÓ

Electric potential difference, often referred to as voltage, is a key concept in understanding how electric fields work. Imagine you have a charged particle moving between two points in an electric field. The electric potential difference \( \Delta V \) between these points tells you how much work is done per unit charge to move that particle. In simpler terms, it measures the energy change, due to the electric field, just like how height measures the energy in a gravitational field.
\[ \Delta V = \frac{-W}{q} \]
Where \( W \) is the work done and \( q \) is the charge. The negative sign indicates that the work done by the field reduces the potential energy stored in the charge. In the exercise, the potential difference was calculated as \( -357.14 \, \text{V} \, \), meaning the potential at the starting point differs by this value from the endpoint.

Work done in physics often refers to the energy transferred when a force is applied over a distance. For electric forces, the work done \( W \) by an electric field on a charged particle is equivalent to the change in kinetic energy of that particle. If the particle starts from rest, its initial kinetic energy is zero. This makes calculating work straightforward:
\[ W = \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
In the given exercise, since the initial kinetic energy was zero, all the work done by the electric force becomes the final kinetic energy, which equates to \( 1.50 \times 10^{-6} \, \text{J} \). This work essentially converts potential energy into kinetic energy, propelling the particle through the field.

Kinetic energy is the energy that a particle possesses due to its motion. When a charged particle is subjected to an electric field, the work done on it changes its kinetic energy. Kinetic energy \( KE \) can be calculated using the formula:
\[ KE = \frac{1}{2}mv^2 \]
This is not needed directly in this exercise, as the particle's mass \( m \) and velocity \( v \) are not given. Instead, we simply know that after moving a certain distance, the particle's kinetic energy \( KE_{\text{final}} \) becomes \( 1.50 \times 10^{-6} \, \text{J} \). The electric field converts potential energy to kinetic energy, allowing the particle to accelerate as it travels through the field.

A particle's charge plays a central role in how it interacts with an electric field. The charge, denoted as \( q \, \) determines both the magnitude and direction of the force exerted on it by the field. In this scenario, the particle had a charge of \( +4.20 \, \text{nC} = 4.20 \times 10^{-9} \text{C} \, \). This positive charge meant it experienced a force in the direction of the electric field.

• A positive charge will move in the direction of the field lines.
• A negative charge will move opposite to the direction of the field lines.

This charge influences calculations like electric potential difference, as seen in the formula \( \Delta V = \frac{-W}{q} \, \) where \( q \) directly affects the result. Understanding a particle's charge helps predict both its trajectory and speed in an electric field.