Lectures on physics

Magnetic vector potential of a rotating uniformly charged shell.

Today we will solve the problem of finding magnetic vector potential of a rotating, uniformly charged spherical shell. We won’t discuss the general idea behind the vector potential (how it follows from Helmholtz theorem, and gauge freedom etc) and how its defined. That will be part of a conceptual lecture and will be available when the same would be created. The offline version is available, but the web version will call for a special priority to be assigned.

The problem is quite well defined. We just need to follow the straightforward method of implementing the basic definitions and carrying out the required steps. But we need to be mindful of the framework in which we need to accomplish these steps.

The framework I am talking about here is the coordinate system we need to set in order to solve the problem. Notice that the problem has been stated in the spherical coordinate system (which has been discussed couple of times in this website). But we need not worry about all the aspects of this coordinate system, we will only pick on those which are immediately applicable to our problem.

While this choice of the system where the polar axis (z-axis, wrt which the polar angle θ is measured in a r, θ, φ spherical coordinate system) coincides with the angular velocity vector ω is very natural, it isn’t the most convenient for carrying out the ensuing integral for the vector potential A.

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.

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.