Why do we need to learn about magnetism and electostatics as two different entities?

Question

So, this year we learnt about electrostatics and both magneto statics and our text book mentions them as deeply interrelated as electromagnetism. After searching more about it, I found that both electric field and magnetic field are the same entities but from different frame of references, that is they are the same manifestations of same thing i.e. electromagnetism. I learned that magnetism was result of electrostatics and special relativity. But why do we pretend like they are completely different things and learn about them as two different entities? should I continue to learn that way? So, when I asked this to my teacher, she replied and I quote," Representing them mathematically require tensors which is a bit tricky, so we usually pretend like they are separate things." What does that mean?

Answer 1

As you have already mentioned, the deep connection between electricity and magnetism is only obvious in the framework of special relativity, which is an entire course on its own. Hence, it is preferred to treat these two phenomena independently for introductory courses. This is especially true for students outside of Physics, such as Electrical Engineering students, since learning relativity doesn't really help them much with the overall objective of their degree/career.
Even for physics students, the connection between the two is only taught in higher level undergraduate courses; when they have covered special relativity on the required level.

About your concern on learning the two subjects independently, treating the two phenomena independently does not give wrong answers if you fix your attention to a specific reference frame, and don't try to change it midway. So don't worry about it.
(Keep in mind however that by independently I mean not as parts of the same entity; as the electric and magnetic fields are still connected through Maxwell's equations for time dependent cases.)

Check out this related question, and also this brilliant video by Veritasium, about "how relativity makes magnets work".

Answer 2

It is because learning electromagnetism as an effect of relativity is very unintuitive without knowing about classical electromagnetism beforehand.

In this case, it is better to learn it in the order it was discovered. First, you start out with simple coulomb's law, leading to gauss law. Then you move on to magnetism, ampere's law and biot savart law (which were derived experimentally), and then writing the magnetic field as the curl of a vector potential. You then move on to magnetic induction, where the changing magnetic field produce an electric field.

It is here, we slowly start noticing the symmetry between electric field, and magnetic fields, by theorizing that a changing electric field can cause a magnetic field. This also fixes ampere's law (which, by itself violated gauss law of magnetism). Now, you write the complete form of the magnetic and potential fields, in terms of the scalar potential and vector potential. Substitute these relations into Maxwell's equation, and then you end up with a completely symmetric formulation of electromagnetism.

Now, when you use special relativity, you'll come to understand that the scalar and vector potential constitute a "4-vector", which leads to the covariant formulation of electromagnetism, completing the unification.

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So, by learning magnetism and electric fields as separate entities initially, you end up having an intuition for the topics and then when you start unifying electromagntism everything starts fitting together like clockwork. As you can see, there's a long journey in between which makes you conceptually clear, and also finding out the reason why special relativity is perfect for unifying electromagnetism