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Analog Electronics: Chapter 5 — Electric Charge and Permittivity

Welcome back to the Analog Electronics series!
In this chapter, we dive into one of the most fundamental concepts in the world of electricity — electric charge — the invisible quantity behind every electric and magnetic phenomenon we study.

We’ll also explore Coulomb’s Law and the idea of permittivity, which together help us understand how materials behave when exposed to an electric field — the foundation of capacitors, dielectrics, and even semiconductor behavior.

Let’s get started 👇

⚡ Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force of attraction or repulsion when placed in an electric or magnetic field. It is one of the most basic and conserved quantities in nature, similar to mass.

Press enter or click to view image in full size

Every atom consists of electrons, protons, and neutrons:

• Mass of electron (me): 9.1 × 10⁻³¹ kg
• Mass of proton (mp): 1.6 × 10⁻²⁷ kg
• Mass of neutron (mn): 1.6 × 10⁻²⁷ kg

Electrons carry a negative charge, while protons carry an equal but positive charge. Neutrons are electrically neutral.

• Charge of electron = −1.6 × 10⁻¹⁹ C
• Charge of proton = +1.6 × 10⁻¹⁹ C

If a proton and an electron are placed 1 cm apart, they experience a force of attraction ≈ 2.3 × 10⁻²⁴ N.

The SI unit of electric charge is Coulomb ©, and the SI unit of force is Newton (N).

🔹 Quantization of Charge

Electric charge is quantized, meaning it exists only in discrete, indivisible packets — not in fractions. The smallest possible unit of charge is that of an electron or proton, represented by e = 1.6 × 10⁻¹⁹ C.

Any observable charge on a body is always an integer multiple of this basic unit:

Q=n×e

where n is an integer.

🔹 Conservation of Charge

Electric charge can neither be created nor destroyed in an isolated system. The total charge before and after any process — whether it’s rubbing, chemical reaction, or nuclear reaction — always remains constant.

Charge may transfer from one body to another, but the net charge of the entire system stays the same.

⚙️ Coulomb’s Law

Coulomb’s Law defines the electrostatic force between two stationary point charges.

It states that:

“The electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.”

Mathematically,

Where:

• F = electrostatic force between charges (in newtons, N)
• q₁, q₂ = magnitudes of the two charges (in coulombs, C)
• r = distance between the charges (in meters, m)
• k = Coulomb’s constant = 8.99 × 1⁰⁹ N·m²/C²

The constant k is related to the permittivity of free space (ε₀) by:

⚙️ Permittivity (ε)

Permittivity is a measure of how easily a material’s internal charges can shift to form tiny dipoles in response to an electric field — or simply, how easily an insulator can be polarized.

There are two types of permittivity:

1. Permittivity in Free Space (ε₀)

In a vacuum (free space), there are no atoms or molecules to polarize.
Even though there is nothing to shift, we still define ε₀ — the absolute permittivity of free space — because:

• It sets the baseline for all electric interactions.
• It defines how strong the electric force is in the absence of any material.
• Coulomb’s Law uses k = 1/(4πε₀) to calculate the force between two charges in empty space.
• It allows us to compare the behavior of materials with free space.

When we put a dielectric (like water or glass) between charges, we compare its permittivity ε to ε₀.

2. Permittivity of a Material (ε)

Permittivity of an insulator or dielectric refers to its ability to polarize when placed in an electric field.

When a dielectric (insulator) is placed in an electric field, charges cannot move freely as in conductors. However, electrons slightly shift opposite to the field, and protons shift slightly in the direction of the field.

This small separation of positive and negative charges forms tiny electric dipoles throughout the material.

The ability of a material to form these dipoles easily is called its permittivity (ε).

• High permittivity: Electrons and nuclei shift more easily → strong dipoles → the material reduces the electric field more.
• Low permittivity: Electrons and nuclei shift less → weak dipoles → the field is reduced less.

🔹 Relative Permittivity (εᵣ)

Relative permittivity (or dielectric constant) is the ratio of a material’s permittivity to that of free space:

It tells us how much the material reduces the electric field compared to vacuum.

🧭 Summary

• Charge is the basic property of matter responsible for all electric effects.
• Coulomb’s Law gives the force between two point charges.
• Permittivity (ε) represents how easily a material polarizes when placed in an electric field.
• Relative permittivity (εᵣ) compares the material’s polarization ability with that of free space.

✨ Closing Thoughts
Understanding electric charge and permittivity forms the foundation for analyzing how electric fields interact with materials — a key principle in designing capacitors, sensors, and semiconductor devices.

Stay tuned for Chapter 6, where we’ll explore the next concept in our Analog Electronics journey!

Analog Electronics: Chapter 4— Intrinsic and Extrinsic Semiconductors

 

In the fascinating world of electronics, semiconductors form the foundation of all modern devices — from the smallest microchips to the most complex integrated circuits. To understand how electronic components like diodes, transistors, and amplifiers work, it’s essential to first grasp what semiconductors are and how their conductivity can be controlled.

Semiconductors

Atoms may combine to form a solid crystalline material through covalent bonding. In silicon, each atom forms covalent bonds with four neighboring silicon atoms, creating a strong and stable crystal lattice. A pure silicon crystal, without any impurities, is called intrinsic silicon.

At room temperature, intrinsic silicon has very limited conductivity. Some valence electrons gain sufficient thermal energy to jump from the valence band to the conduction band. When this happens, free electrons are generated in the conduction band, and vacancies are created in the valence band. These vacancies are called holes.

If a voltage source is applied across intrinsic silicon, the thermally generated free electrons in the conduction band will move toward the positive terminal of the voltage source. This movement produces current in the material, which is called electron current. Simultaneously, holes in the valence band contribute to conduction. When an electron from a neighboring atom moves to fill a hole, it leaves behind a new hole. This movement of holes generates hole current.

Thus, intrinsic silicon shows conduction through both free electrons and holes, but the conductivity is very low.

Extrinsic Semiconductors

The conductivity of semiconductors can be greatly improved by a process called doping, in which controlled amounts of impurities are added to pure silicon. Depending on the type of impurity added, the resulting material can be either n-type or p-type semiconductor.

N-Type Semiconductor (Pentavalent Impurity)

When a pentavalent impurity (an atom with five valence electrons, such as arsenic, phosphorus, bismuth, or antimony) is added to silicon, four of its valence electrons form covalent bonds with four neighboring silicon atoms. The fifth electron, however, does not participate in bonding and remains loosely bound to the dopant atom.

This extra electron requires very little energy (about 0.01 eV) to move into the conduction band, which is far less than the 1.1 eV required to break a silicon-silicon covalent bond. At room temperature, almost all these donor electrons are free to move, creating a large number of charge carriers without disturbing the crystal lattice.

As a result, n-type semiconductors exhibit much higher electrical conductivity at room temperature compared to intrinsic silicon, where only a few valence electrons can thermally jump to the conduction band. In n-type semiconductors, electrons are the majority carriers, while holes are the minority carriers.

P-Type Semiconductor (Trivalent Impurity)

When a trivalent impurity (an atom with three valence electrons, such as boron, indium, or gallium) is added to silicon, each dopant atom forms covalent bonds with three neighboring silicon atoms. This leaves one bond incomplete, resulting in the creation of a hole.

At room temperature, electrons from neighboring silicon atoms can move to fill this hole, which in turn creates a new hole at the position from where the electron moved. In this way, holes effectively move through the crystal lattice and act as charge carriers.

Thus, in a p-type semiconductor, holes are the majority carriers, while electrons are the minority carriers.

Summary

Intrinsic semiconductors are pure crystals with very low conductivity, where current is generated only by thermally excited electrons and holes.
Extrinsic semiconductors are doped with impurities to enhance conductivity.

• Pentavalent impurities create n-type semiconductors, where electrons are the majority carriers.
• Trivalent impurities create p-type semiconductors, where holes are the majority carriers.

Conclusion

Semiconductors are the backbone of modern electronics. By understanding the difference between intrinsic and extrinsic types, we unlock how materials can be engineered to conduct electricity in controlled ways — forming the base for diodes, transistors, and integrated circuits.