As we know that, learning of physical concepts is a step by step process, no short cuts, no skipping, no tricks, in this process are helpful. It has been observed in experiences that students face the problems to understand the advance sciences, when they study and reads it in detail with the mathematics. The reasons may be many, but lacking of connectivity with the fundamental physical concepts are important, which plays the role. In lower classes, students starts their learning by reading the definitions, laws, etc. and related formula, if there is any in to the concern topic. Here, they also learn about the relevant physical picture(s) of a standard law or concept too. So, development of physical picture(s) of a concept (Definitions, Laws,etc.) is the main key in lower classes and then after mathematical formula.
As the students succeeded in higher class they also study maths and learn tricks to solve its problems but rarely they learn, role of mathematics in general life; means day to day problems or physical concepts on which they are based. They see mathematics just in the form of some symbols and equations from the beginning and don’t focus on its physical origin and applications in daily life. A major problem from my perspective. In this learning process and to get higher education students choose a specific course/subject/degree of science (s) for various life purposes. Some students remain aware about the learning of lower classes physical concepts, pictures and mathematical formule, while some forgets with the passage of time. No problem at this point, it is natural phenomenon with individual memory. This is not problem because when they read, listen and watch about its, again they get the related required information
At the stage of higher classes, when students reads the subject (s) in details with all relevant information, mathematics helps to explain the physical pictures of different stages, specially in Physics course. In the theoretical development of any particular topic(s), we assume many points and takes parametric help to get the required result. No any advance topic(s) [advance topic means, proper details of a physical phenomenon] can be derived with out the help of one or many supporting physical concepts (SPCs), if these SPCs are clear to the student, he/she will not face any problem to understand that topic. Also, he/she can use it in many applications or can develop other application(s) for the betterment of people’s life. If SPCs are not clear then obviously he/she will face the problems.
What is Supporting Physical Concepts (SPCs)? The SPCs are those independent small physical concepts which are helpful not only in mathematical derivations but for the understanding of the topics too. In case of Susceptibility the following are the Supporting Physical Concepts (SPCs),
1. Atomic Dipole and its Magnetic Moment Concept
3. Types of Magnetic Materials
4. Working of Electromagnet
5. Unit system (SI or CGS)
6. Magnetic field and Magnetic Field Intensity Concepts
7. Nature of the Force on magnetic material (here liquid) in the presence of external magnetic field
If you have answers of these supporting physical concepts (SPCs) then you can explain anything related to the susceptibility but for mathematical derivation differentiation, integration and limits also plays the role. So that knowledge is also must.
(A) In Hall Effect, the following are the Supporting Physical Concepts (SPCs);
1. Lorentz’s Force
2. Flemming’s Left Hand Rule
3. Basic idea of Electric Field and Magnetic Field
4. Properties, Type & Characteristics of Semiconductor Material
(B) In LASER understanding, the following are the Supporting Physical Concepts (SPCs);
1. Basic Atomic Structure, Orbital and Shells idea
2. Energy levels and their Life time
3. Electronic Transition and Their result in terms of Photon Emission
(C) In Electrodynamics, the SPC’s are four basic laws in integrals and differential forms known as Maxwell’s Equations.
1. Gauss’s Law in Electrostatics
2. Gauss’s Law in Magnetism
3. Faraday’s Law
4. Ampere’s Law
Here, I have told only about the Physics Supporting Physical Concepts (SPCs) for some topics. Similarly one can see in other sciences too. Also, there is no limitation of number to addition and removing the SPCs as mentioned above for a particular topic. But in general a 4-6 SPCs we observe for any topic. This is just an observation to make the topic more clear and understandable to the students. Also students learn the connectivity of the physical concept which further helps them to build the analysis ability. But a question rises here in my mind, does the students are aware enough to find the SPCs itself for any particular topic? The answer is most probably no, I think, in primary stage of the subject its little difficult to know by the students that which SPCs are useful for the topic. So a teacher can help, guide here to find the relevant SPCs before delivering the lecture(s) in classroom.
NOTE: These are my personal and experienced based views may be vary for other subject specific experts. I found recently it very useful and supportive in the learning of the students.