Semiconductors and charge carriers: the copper atom's electronic configuration. There are 29 electrons and 9 protons in the copper atom which makes it electrically neutral. Together with 28 electrons in the first 3 shells ( K, L, M ) and the 28 protons in the nucleus the copper atom's core has a net charge of + 1 e. The electron in the outermost N shell has only 1 electron known as the valence electron. Photo-Credit: mdashf.org

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Semiconductors and charge carriers (L-I)

Analog electronics and applications

Conductors, semiconductors and holes as charge carriers

Topics covered in this lecture

A. Conductors

B. Semiconductors

C. Holes

D. Intrinsic semiconductors

Conductors: A conductor is the name of a material which is a good conductor of electricity. Copper ( Cu ), Silver ( Ag ) and Gold ( Au ) are examples of materials which are good conductors of electricity, in other words they are known as conductors. 

A natural question arises as to why copper is a good conductor of electricity. Such a fact can be understood from its electronic configuration.

Electronic configurations are a good way to understand the physical as well as chemical properties of materials. A great deal of our modern understanding of materials and their properties are based on the detailed electronic configuration facts of the same.  

The copper has 29 electrons in its atom. That means it has an equal number of protons. It has two isotopes, one has 34 and the other has 36 neutrons. Isotopes are the same chemical element having 2 or more than 2 different types of nuclei, due to difference in the number of neutrons. As a whole copper atom is electrically neutral. 

The 29 electrons are distributed into shells or orbits. Consequently the first orbit has 2, 2nd orbit has 8 and 3rd orbit has 18 electrons. There is only 1 electron in the outermost orbit of the copper atom. 

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3 most important lattice types, the simple cubic (sc), the body centered cubic (bcc) and the face centered cubic (fcc) types

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Fundamental types of crystal lattices and their symmetry operations

Fundamental types of crystal lattices and their symmetry operations.

Topics covered
a. Types and classes of crystals,

b. Symmetry operations in crystals

In this lecture we will follow through our basic knowledge gained in the last lecture. — lecture — I, II, and shed light on the most interesting properties of crystal lattices, viz. their symmetry properties. Based on their properties we will classify them into various types and classes.

ii. Lattices satisfy additional symmetry operations. But due to the constraint of translational symmetry the total number of symmetry operations that the lattices can satisfy is reduced to a minimum.

iii. This means in 2-dimensional lattice constructs we have only 5 types of lattices which satisfy additional symmetry operations. In 3-dimensional geometry there are a total of 14 classes of lattices.

iv. Thus in 3-dimensional lattices the 14 classes of Bravais lattices are categorized into 7 types or systems of fundamental lattices.

v. The extra symmetry operations are

various rotations,
inversion about a space point and
reflection about a plane passing through a lattice point or
their possible combinations.

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The northern light or aurora is an electromagnetic phenomenon, produced due to motion of charged cosmic particles entering earth's magnetic field.

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Helmholtz theorem in electrodynamics, Gauge transformation.

Electromagnetic theory, lecture — IV

Topics covered in this lecture

a. Helmholtz theorem — in electrodynamics

b. Gauge transformation — of scalar and vector potential in electrodynamics

c. Coulomb and Lorentz gauge

All electromagnetic theory lectures of this series, will be found here (https://mdashf.org/category/electromagnetic-theory/)

In our previous lecture — lecture — III, we discussed in quite detail, the problem of electrostatics and magneto-statics.

We understood how deeply the Helmholtz theorems formulate the entire question of these two branches of electromagnetic phenomena.

But static problems are not sufficient for any rigorous treatment of the electromagnetic theory.

We promised in that lecture to study how Helmholtz theorems lend their magical power to understand the most general nature of electromagnetic phenomena.

In this lecture we will study precisely the applicability of Helmholtz theorems to the problem of electrodynamics and we will see how it leads to a great deal of success in advancing the ability to solve electromagnetic problems of a great variety. 

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This image shows the fabulous colors cities wear at night. And it all comes from electromagnetic waves. Our topic today is an attempt at understanding the deeper formal frame work of electromagnetic waves.

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Helmholtz theorem. Scalar and vector potentials

This lecture develops the formalism of electrodynamics in a very methodical way.

It covers the following topics in detail.

A. Formalism of electrodynamics — fundamental theorem

B. Application of Helmholtz theorem — to electrostatics

C. Application of Helmholtz theorem — to magnetostatics

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Boundary conditions on electric and magnetic field: When electric or magnetic fields go across the boundary of material media their values might or might not change. There are 4 possibilities and we derive them in this article. These values depend upon the surface current charge densities and the volume charge densities present on the surface of the media. Accordingly the tangential and normal components of electric and magnetic fields have 4 different possibilities. 2 of these change and are named as discontinuous while the other two don't change and are therefore called as continuous. Photo Credit: mdashf.org

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Boundary conditions on electric and magnetic fields.

Electromagnetic theory, Lecture — II. 

Boundary conditions on Electric and magnetic fields in Maxwell’s equations

Topics covered

A. Summary of Maxwell’s equations — in free space and in material media

B. Integral forms of Maxwell’s equations — by application of vector calculus

C. Derivation of boundary conditions — on electric and magnetic fields

In the last lecture we formulated the Maxwell’s equations, for free space as well as any material medium in their differential form.

Remember that we say free space to mean that the sources of charge densities and sources of current densities that experience our field vectors, viz. $latex vec{E}$ and $latex vec{B}$ — which are produced by other source densities of charges and currents, are non-existent.

That is there is no hindrance or onlookers our $latex vec{E}$ and $latex vec{B}$ fields meet on their way when they go on a sojourn, in that space. I also hear they call it by the name vacuum. As far as I know I testify, there is no difference between vacuum and free space.

Vacuum simply means for our purpose and many others, there is no glimpse of matter in the space of consideration. It is therefore the simplest of situation to harp on, before we can target our intelligence for achieving more complicated scenario, and yes there certainly are such situations and they take most of our coveted attention in asking us to solve them. 

And sooner than later we would be on our toes trying to grasp the burden the more complicated situations would unleash our way. For the time being we focus on free space which means the sources are zero.

Again by sources we mean, not the sources that produce our vector field $latex vec{E}$ and $latex vec{B}$ but the ones that interact with them, in the path of our fields. 

read more Boundary conditions on electric and magnetic fields.