Confusion created by notation in E&M

[leroyjenkens]

I just started an E&M class and right from the beginning the notation seems so confusing it has to have been done as a joke.
Trying to do a problem I run into about 10 different r's I have to keep track of.
Capital R
Lower case r
Lower case r prime
The r in spherical coordinates
The "squiggle" r (As this professor calls it. Never heard that before this class, but he talked about it like everyone knows. It's just a cursive r from what I can tell.)
"Squiggle" r hat
Normal r hat prime
"Squiggle" r with an arrow over it.
The normal r with an arrow over it
Normal r with an arrow over it prime

So when I see an equation with 3 or 4 different r's in it, my head just explodes. Why is it like this? And am I the only one who thinks this makes it confusing?

 

[ObsessiveMathsFreak]

This is what happens when you restrict yourself to the latin Alphabet. Try using Greek and Cyrillic letters if you run out.

 

[0xDEADBEEF]

There is a weird fascination with symmetry and making letters look the same. Euler angles were introduced to me with $$\xi, \zeta, \eta$$ as indices. Integration by parts uses u and v, there is p and q for Lagrange mechanics. i and j for electrodynamics. {j,k,l} and {x,y,z} might not be so bad, but j and l are close in some handwriting as well as x and y. These things will never be reformed because we are still citing papers from 1910. The worst we had was in the discussion of collisions where I think r-prime-prime-tilda-hat was the vector of the second particle after the collision in center of mass coordinates.

 

[PhilDSP]

I find it works extremely well when dealing with an unfamiliar notion to relabel each variable to something that makes sense to you, like $m_{electron}$ instead of $Z_0$ for example. Then rewrite all of the equations and work with them until you feel comfortable and translate back as required.

 

[PJC01]

I can understand your frustration with the notation in E&M. It can definitely be overwhelming and confusing, especially when there are multiple variations of the same letter being used. However, it is important to remember that notation is a crucial aspect of science and mathematics. It allows us to communicate complex ideas and equations in a concise and standardized manner.

In the case of E&M, the different r's are used to represent different quantities or variables. For example, capital R may represent the radius of a charged object, while lower case r could represent the distance from the center of that object. The use of r prime indicates a change in that variable, similar to how a derivative is denoted in calculus.

The use of different r's in spherical coordinates is necessary because it represents a different coordinate system than the traditional x, y, z system. And the "squiggle" r with an arrow over it is used to represent a vector quantity, while the normal r with an arrow over it represents a unit vector in the direction of r.

While it may seem overwhelming at first, with practice and familiarity, you will become more comfortable with the notation. It is important to remember that it is meant to make things easier to understand and communicate, not to confuse or frustrate. And if you have any questions or need clarification, don't hesitate to ask your professor or classmates for help. They were all beginners at one point too and can offer valuable insights and tips. Keep at it, and soon enough, the notation will become second nature to you.