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An electron is a tiny subatomic particle carrying a negative charge. When an electron is placed in a uniform electric field, it experiences a force due to the field, which causes it to accelerate. The direction of this acceleration is determined by the direction of the electric field and the charge on the electron. Since electrons are negatively charged, they move in the direction opposite to the electric field lines.

In our exercise, the electron is initially at rest, meaning its starting velocity is zero. When released in an electric field, it accelerates upwards over a certain distance and time. Understanding this motion involves concepts of charge and force:

• An electric field exerts a force on charged particles.
• This force is calculated using the product of the charge and the field strength: F = qE.
• For an electron, with charge \(q = -e\), direction of force will be opposite to that of field.

As the problem states a vertical upward motion over a specific period, we can derive information about the electron's path from this acceleration.

Kinematic equations are useful tools in physics for describing motion. They relate different physical quantities such as displacement, time, and acceleration. In the context of our exercise, the motion of the electron is described through these equations.

The relevant kinematic equation for this problem is: \[ a = \frac{2 \cdot (d - u \cdot t)}{t^2} \] Where:

• \(a\) is the acceleration
• \(d\) is the distance traveled
• \(u\) is the initial velocity (zero in this scenario)
• \(t\) is the time taken

By plugging in the time and distance values, we find the acceleration the electron undergoes. This acceleration, resulting from the electric force, is crucial in establishing the magnitude of the electric field acting on the electron.

In typical problems involving objects in motion near Earth's surface, gravity is a significant factor to consider. However, in the case of an electron, due to its very small mass, the effects of gravity may be negligible when compared with the forces from an electric field.

The gravitational force acting on the electron can be determined using the formula: \[ F_g = m \cdot g \] Where:

• \(m\) represents the mass of the electron
• \(g\) is the acceleration due to gravity, approximately \(9.81 \, \text{m/s}^2\)

By evaluating this force against the considerably larger electric force \(F = m \cdot a\) due to the electric field, we find that the gravitational force \(F_g\) is much smaller. Thus, its influence on the electron's motion is insignificant, allowing us to justify generally ignoring it in such scenarios.