91Ó°ÊÓ

Kinematics is the study of motion without considering the forces that cause it. In this exercise, we're interested in describing the motion of an electron as it enters an electric field.
When analyzing motion, we often use key quantities like velocity, time, acceleration, and displacement. Here, the initial velocity of the electron is \(2.60 \times 10^{6} \, \text{m/s}\). As the electron travels through the electric field, its speed is reduced until it stops momentarily.
To find how far the electron travels before stopping, we use one of the kinematic equations:

• \(v^2 = u^2 + 2ad\)

This equation connects the initial speed \(u\), final speed \(v\), acceleration \(a\), and distance \(d\). By substituting in known values and solving for \(d\), we gain insight into how the electron behaves in the electric field.
This analysis is crucial as it helps us understand how charged particles move in electric fields, which is a fundamental concept in physics.

Kinetic energy is the energy possessed by an object due to its motion. The faster an object moves, the greater its kinetic energy. When an electron enters an electric field and begins to decelerate, it loses kinetic energy until it stops.
The initial kinetic energy \(KE_i\) of the electron is calculated using the formula:

• \(KE_i = \frac{1}{2}mv^2\)

where \(m\) is the mass of the electron, and \(v\) is its initial speed.
As the electron travels through the short 8 mm electric field region, we are interested in knowing how much of this initial kinetic energy is lost.
To calculate the fraction of the energy lost, we use the difference between the initial kinetic energy and the kinetic energy when the electron has traveled 8 mm. This helps us understand how fields influence the energy of moving particles, which is essential in both theoretical and applied physics.Understanding kinetic energy changes allow scientists to design technologies manipulating electron movement, such as in particle accelerators.

Newton’s Second Law is a central principle in physics. It describes how the acceleration of an object is related to the net force acting on it and the object's mass. This law is expressed with the equation:

• \( F = ma \)

Here, \(a\) is acceleration, and \(m\) is the mass of the object.
In the context of this problem, we apply Newton's second law to quantify how the electric force affects the electron.
The force on the electron due to the electric field is calculated as:

• \( F = eE \)

where \(e\) is the charge of the electron, and \(E\) is the electric field strength.
This force causes the electron to decelerate, changing its motion as predicted by the laws of kinematics.
By knowing this acceleration, we can determine how quickly the electron will stop when it enters the field. This concept shows us the unifying power of Newton's laws — they help predict the behavior of objects, from everyday items to subatomic particles, under various forces.