Electron Under An Electric Field

Electrons are subatomic particles with a negative charge of about 1.602 × 10-19. The charge is equal in magnitude to that of the positive charge on a proton but has an opposite sign.  An electron under an electrical field feels a repulsive or attractive force. When a positive electrical field is applied to the metal, it will generate an attractive force on the electrons. The reason is the attraction between the two opposite charges. As a result, electrons will escape from the metal due to this attractive force. 

In the same way, when electrons are exposed to photons, they are ejected from the metal surface. So, why does that happen? Let’s discuss the photoelectric effect in detail to know the reason behind this phenomenon. Also, read this electron under an electric field UPSC notes for more in-depth information on the topic. 

What is the Photoelectric Effect?

The phenomenon of the Photoelectric Effect was first observed by Heinrich Rudolf Hertz in 1887. In this quantum electronic phenomenon, when light incidents on metal surfaces, it causes the release of electrons from the surface of metal materials. 

What are photons? Photons are the smallest particles of light that can travel through space. They have energy and momentum. Thus, the photoelectrons (electrons emitted from the metal) dislodge from a particular metal due to the incident photons. Thus, the process is known as photoemission. Albert Einstein proposed the whole explanation. 

According to his theory, the photoelectric effect starts when continuously light particles (photons) that exceed a threshold energy strike the metal. They are the carriers of electromagnetic fields carried in discrete quantized packets. Changes occur in the kinetic energy of the electrons due to the transfer of energy from the light particles (photons). Thus, the ejection of electrons occurs, but it depends on the frequency of the light waves. The higher the frequency of light waves, the higher the energy it carries. For example, blue light has a greater frequency than red light. Hence, it carries more energy to overcome the attractive forces. 

Let us understand it through Planck’s equation:

E = hv = hc/λ

Where,

E = energy of the photons

ν = frequency

h = Planck’s constant = 6.63 × 10–34 Js

c = speed of light = 3.0×108 ms−1

λ = wavelength of the incident light

Laws of photoelectric effect

There are a total of four laws of the Photoelectric Effect. They are as follows:

1. For a light of a certain frequency, the number of photoelectrons emitted is directly proportional to the intensity of the light, and saturation current is directly proportional to the incident light’s intensity. 
2. There is some maximum kinetic energy of the photoelectric which is independent of intensity and directly proportional to the frequency of light.
3. For a given surface, the emission of photoelectrons occurs if the frequency of light is equal to the threshold frequency. The emission will stop if the frequency is lower than the threshold. 
4. Time does not lag between the incident of light and the ejection of electrons.

Motion of electron under electric field

An electron under an electric field moves in a particular direction when two parallel plates with uniform electric fields are used. It will move towards the positively charged plate through electronic holes and away from the negatively charged plate. The electron’s motion occurs with constant velocity and at the right angle to the field produced between the plates. Therefore, the trajectory is the parabola. 

But, the direction is opposite in comparison with the electric field vector. Thus, the force will be accelerating the electron, which can be evaluated using Newton’s second law. The more they accelerate, the more they lose energy in the form of radiation. Hence, the motion of the electron under an electric field slows down as the potential energy of the electron decreases.

There is the difference in electric potential energy between the plates and is denoted by V. The following expression gives the magnitude of the force on an electron under an electric field:

F = qE

Where, 

F = force on an electron

q = charge of an electron

E = Electric field between the

plates

Also, V = Ed

Where, 

V = Potential difference between the plates 

E = Electric field between the

plates

d = Distance between two plates

Hence, F = eV/d

Therefore, you may now find out the force on the electron under an electrical field with the help of this equation. You can understand the motion of electrons in a better way through some electrons under an electric field examples.

Suppose an electron of charge q in a TV set is accelerating. There is some potential difference V between the cathode and anode, which is placed at a distance d. The given electric field between the anode and cathode E. This can be used to calculate the force on an electron in this uniform electric field.

Conclusion

Learning about the concept of electron under an electric field can help give you an understanding of how the photoelectric effect and the motion of electrons under an electric field work in modern physics. One of the best ways to understand the concept is through the four laws of the photoelectric effect, and then applying the concepts through formulae to solve problems.