91Ó°ÊÓ

When an electron is subjected to an electric field, it experiences a force that causes it to accelerate. Here, since the electron is released from rest, its initial velocity is zero. The acceleration (\(a \)) can be calculated using kinematic equations. The key point to remember is that as a charged particle, an electron will accelerate in response to electric forces.
Given the provided exercise, the acceleration is massively large, around \(1 \times 10^{12} \, \text{m/s}^2\). This value comes from the equation \( s = ut + \frac{1}{2}at^2 \), where displacement \(s\), time \(t\), and initial velocity \(u\) are known.
Because the electron doesn't have a large mass, even a relatively small electric field can cause significant acceleration.

In a uniform electric field, the electric force exerted on a charged electron is constant in magnitude and direction. This consistency means that an electron in such a field will experience uniform acceleration.
The magnitude of the electric field \(E\) is found using the relationship between force \(F\) and charge \(q\), expressed as \(E = \frac{F}{q}\).

• The electron's charge is \(-1.6 \times 10^{-19} \, \text{C}\), and using the derived force \(9.11 \times 10^{-19} \, \text{N}\), the field is calculated as \(5.69 \, \text{N/C}\).
• Direction is also critical: since electrons are negatively charged, they move opposite to the electric field's direction. Hence, if the electron moves upward, the electric field is directed downward.

Understanding that the field affects movement all through the same path and force is pivotal in analyzing and solving related problems.

Kinematic equations are foundational tools in physics that describe the motion of objects under constant acceleration without considering forces. They help us determine how an object's position, velocity, and time relate when it is subjected to uniform acceleration.
For this problem, the kinematic equation \(s = ut + \frac{1}{2}at^2\) was used to find the acceleration of the electron, given the displacement and time, with initial velocity at zero.

• In scenarios like this, the direct relationship between time, displacement, and acceleration allows solving for one variable when the others are known.
• They simplify understanding motion and form the basis for more complex physical problems.

Mastery of these equations will enable students to solve various problems involving motion, particularly in electric fields, as seen here.

In certain scenarios in physics, some forces can be disregarded due to their minor influence compared to others. Here, the gravitational force acting on the electron is negligible compared to the electric force.
By calculating the gravitational force \(F_g = mg\) and comparing it with the electric force \(9.11 \times 10^{-19} \, \text{N}\), it's clear that gravity, calculated as \(8.93 \times 10^{-30} \, \text{N}\), is minuscule.
The huge difference, nearly twelve orders of magnitude, shows gravity's effect is practically zero:

• Electron's small mass greatly reduces gravitational force effect.
• It's often customary to ignore forces that are orders of magnitude weaker, simplifying the problem.

By omitting such forces, calculations become more straightforward, and this approach can often be justified quantitatively, as shown.