The difficulty of learning Electromagnetism vs Classical Mechanics

In summary, the consensus seems to be that electromagnetism is more difficult than classical mechanics. The mathematics and application of continuum mechanics may be more difficult.
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vco
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There was an old thread comparing the difficulty of classical mechanics and electromagnetism. The consensus was that electromagnetism is more difficult, and substantially so according to some. The thread was no longer open for replies, but it got me suspecting that we're comparing apples to oranges here.

Comparing the difficulty of classical mechanics to that of electromagnetism is a bit unfair if we limit ourselves to particle mechanics (point masses, springs, etc.), which is often the scope of mechanics courses for undergraduate physics students. The electrical counterpart of particle mechanics is circuit theory, not electromagnetism. Electromagnetism is a field theory and therefore its mechanical counterpart is continuum mechanics (elasticity, fluid dynamics).

While electromagnetism certainly is conceptually more difficult than continuum mechanics, I believe the mathematics and application of continuum mechanics are more difficult. Richard Feynman appeared to agree (The Feynman Lectures on Physics, Volume II, Chapter 39. Elastic Materials):
... somewhat more difficult to do than the corresponding problems in electromagnetism. It is more difficult, first, because the equations are a little more difficult to handle, and second, because the shape of the elastic bodies we are likely to be interested in are usually much more complicated. In electromagnetism, we are often interested in solving Maxwell’s equations around relatively simple geometric shapes such as cylinders, spheres, and so on, since these are convenient shapes for electrical devices. In elasticity, the objects we would like to analyze may have quite complicated shapes—like a crane hook, or an automobile crankshaft, or the rotor of a gas turbine.
 
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Indeed, continuum mechanics is more difficult than electrodynamics, because it's at the start a non-linear theory already for the most simple case of perfect fluid dynamics, while you get pretty far in electrodynamics as a linear theory since linear-response theory for the constitutive relations of matter (##\epsilon##, ##\mu##, ##\sigma## as material constants or functions of frequency in Fourier space of the matter).
 

Related to The difficulty of learning Electromagnetism vs Classical Mechanics

1. What is the main difference between learning Electromagnetism and Classical Mechanics?

The main difference between learning Electromagnetism and Classical Mechanics is that Electromagnetism deals with the interactions between electric and magnetic fields, while Classical Mechanics deals with the motion of objects under the influence of forces.

2. Which subject is considered more difficult to learn, Electromagnetism or Classical Mechanics?

This is subjective and can vary from person to person. However, many students find Electromagnetism more difficult due to its abstract concepts and complex mathematical equations.

3. Are there any similarities between Electromagnetism and Classical Mechanics?

Yes, there are some similarities between the two subjects. Both Electromagnetism and Classical Mechanics are based on fundamental laws and principles, such as Newton's laws of motion and Maxwell's equations.

4. What are some tips for understanding Electromagnetism and Classical Mechanics?

Some tips for understanding these subjects include practicing problem-solving, breaking down complex concepts into smaller parts, and seeking help from a tutor or teacher when needed.

5. How can learning Electromagnetism and Classical Mechanics benefit me as a scientist?

Both Electromagnetism and Classical Mechanics are fundamental to many areas of science and engineering. Understanding these subjects can provide a strong foundation for further studies in fields such as physics, electrical engineering, and materials science.

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