# Teaching

## Problem 5.13 Application of Ampere’s Law.

Yesterday we saw an interesting application of the Ampere’s Law (– in magnetostatics and sometimes called Ampere’s circuital law also) for the infinite uniform surface current. Today we will see yet another display of the elegance and efficacy of this law in the following problem. This problem is inherited from Griffith’s text on Electrodynamics (3rd edition)

I have tried to be a bit more explanatory than the basic solution available (in instruction manual, if you have a copy). Thats the whole idea of this labor I have taken up. I also strongly suggest anyone who want to sharpen his saber to try the problem on his/her own effort before looking into the solution. That way one can prepare oneself for the pitfalls of one’s own understanding before taking up help and damaging the opportunity of developing of a better sense of solving such problems.

A steady current I flows down a cylindrical wire of radius a. What would be the magnetic field outside the wire and inside of it? We need to find the same in two different scenarios given.

Here are the two different scenarios.

A. Its a surface current density on the outside surface and its uniform across the surface.

B. Its a volume current density and its distributed in the volume of the  wire, but this time its not uniform. In-fact the volume current density J is directly proportional to s; the distance from the axis of the wire where we are referring the value of J.

## Maxwell Boltzmann distribution for a classical ideal gas

i. We assume a dilute gas which is enclosed by a thermally insulated container on all sides.

Dilute gas in a thermally insulated container: Dilute means concentration of gas molecules is low. Insulated implies there is no reasonable flow of heat energy across the walls of the container.

ii. Each molecule is assumed to be a hard sphere which moves randomly in all directions such that its velocity vary from – infinity to + infinity.

Hard sphere: Remember a hard sphere is a classical analogy of a rigid sphere whose surfaces do not deform when an external object comes into contact. This essentially means the incoming object is scattered elastically that is without loss of kinetic energy, only momenta magnitude and directions are changed in accordance with the conservation of linear momentum.

iii. When molecules collide they do not lose energy or time. They bounce off each other so that ‘energy’ and ‘momenta’ are conserved.

We would like to obtain an expression for velocity distribution function. That is we would like to know the fraction of molecules having velocity between v to v+dv for all possible values of velocity.

For this we assume an ensemble of molecules in equilibrium. The ratio of number of molecules in a velocity range to the total number of molecules N gives the probability of finding a molecule in that velocity range.

v. The “phase space” of the ensemble of molecules is defined by a 6 N dimensional space, which constitutes of 3 N spatial components and 3 N velocity components of the N molecules in equilibrium. For a more advanced concept of phase space check the following statistical mechanics lecture.

## If you would like to become a nuclear physicist, what you would like to know about the nucleus first?

A. structure of the nucleus

Every atom consists of a dense positive central core of mass, known as nucleus. Its size is much smaller compared to the size of the atom, nut nonetheless it contains almost all of the mass of the atom.

The nucleus is made of only neutrons and protons. — These are collectively known as nucleons.

Nucleons are not the smallest constituents of matter. — In-fact nucleons are made of different combinations of 3 quarks, of which only two of the quarks can be of the same type.

Combinations of 3 quarks which form into a bound state of material system are known as baryons. We will study about baryons in the last part of this lecture series.

Thus baryons are a naturally occurring collective matter, built from 3 quarks, where the 3 quarks interact among each other, but can’t escape this bound state of formation, even under the impact of tremendous force.

This fact is known as asymptotic freedom, such freedom is only a dream for them, and for us. This is possible in principle, when the distance of separation between them can be made infinite, in order to weaken the existing attractive force between them, to zero.

## Semiconductors and charge carriers

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.

## 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.