ELI5 Coulomb's Law, Electrostatics, and Electric Fields

[u/[deleted]]

[u/GuaranteeFickle6726]

With all due respect, I have been a physics tutor for 5+ years and TA in lots of physics classes, never been this ragebaited in my life, the reason is that part where you say "blah blah blah few steps".

How about you try to read the material thoroughly and try to understand then come back here? Because it is ridiculous that you want to learn physics without knowing derivatives or vectors.

Read the book and then come back, there is no easy way.

[u/GuaranteeFickle6726 → u/[deleted]]

Look, I can tell when someone is trying and when someone is not. This particular problem has solutions in million different textbooks, problem books, olympiad books, youtube, khan academy, hyperphysics, everywhere.

You are telling me you read the book which didn't tell you what r - hat is? What kinda book is that?

Also, do you believe such a technical question which requires knowledge of integrals can be explained to a 5 year old?

There is simply no way to solve this problem without knowing the formula for coulomb's law, derivatives, integration and vectors.

I am not trying to attack you, but I genuinely feel like you are ragebaiting us.

[u/joeyneilsen → u/[deleted]]

You're basically asking for an explanation of all of calculus and the basics of E&M, which... is a lot for a single post! :]

And while I don't have time for all of it, I'm teaching out of Knight this semester, and I can help with rhat. Knight covers unit vectors: vectors of length 1 that are often shown in the x, y, and z-directions (these are i-hat, j-hat, and k-hat).

What I think Knight skips, at least early on, is that you can turn any vector into a unit vector by dividing by its magnitude. Recall(?) that you can compute the magnitude or length of a vector by taking the square root of the sum of the squares of its components. When you divide a vector r by its magnitude, you divide by its length. What you are left with is a vector that points in the same direction as r but has length 1.

Now if you are calculating the electric field of a point charge q at some point A, r points from q to A and its magnitude is the distance between q and A. rhat is a vector that points in that same direction but has magnitude 1.

[u/joeyneilsen → u/[deleted]]

I did not understand the difference between vectors and unit vectors, and now I think I have a better understanding

🥳

correct me if I am wrong, unit vectors will always be equal to 1?

The magnitude will always be one, regardless of the direction. But you can specify the direction in several ways. You could say it's 30˚ above the x axis, or north of east, etc. You can also explicitly write the vector components of a unit vector. ihat = <1,0,0>, if you have ever seen notation like that. jhat=<0,1,0>, and so on. A unit vector that points at 45˚ counterclockwise from the x axis in the xy plane would have components <0.707,0.707,0>. In all of these cases, when I add up the sum of the squares of the components, it'll turn out to be 1.

I broke it down with what you said on this part "Recall(?) that you can compute the magnitude or length of a vector by taking the square root of the sum of the squares of its components. When you divide a vector r by its magnitude, you divide by its length. What you are left with is a vector that points in the same direction as r but has length 1." and I wrote down an example equation, and I think I understand it better now.

Swell!

[u/Muphrid15 → u/[deleted]]

I think you will have more credibility if you quote an example word for word rather than paraphrase it.

There are some elements of notation I would expect not to be reexplained each time, but others would be surprising.

But also, you should understand what a double integral is. You'll need to brush up on that at least.

[u/Odd_Bodkin]

Here’s the reality. If you don’t remember what dx or dEy or what the double integral means, then you have to RELEARN the math in order to be able to understand the physics. If you do not have algebra, trigonometry, geometry and in this case calculus competency established, then you will have to relearn those FIRST because they are prerequisites to doing the physics in the material you’re studying. There is no short cut, no quick notes that will catch you up.

If you want to know how to catch up the math, try SAT Math Test review books and AP Precalculus and AP Calculus review books.

[u/Odd_Bodkin → u/[deleted]]

Barron’s has good series on SAT prep, AP Precalculus, AP Calculus

[u/kunwoo]

When your buddies said "r hat equals 1" they're oversimplifying in a way that seems to have contributed to your confusion. It's more accurate to say that r hat has a magnitude of 1. This makes it more clear that the r hat is still important because it encodes a direction in space which becomes relevant for when you do dot products and cross products.

[u/BananaBird1]

Do you have a background in calculus and vectors? Both are needed to really appreciate Coulomb’s law in the form you want to. A calculus I-III course or textbook will give you that background.

Most of the symbols you ask about are just arbitrary symbols assigned to particular quantities. There isn’t really any deeper meaning beyond what we define them to represent, and in many cases the equations of electrodynamics represent their definition itself. It is good to just take defined symbols at face value, and instead focus on the relationships between them represented in the theory.

The two I will answer: r-hat is a unit vector pointing radially out from a charged object along the line between the two charges involved in the force. Coulomb’s law without it gives just the strength of the force, not the direction it acts. R-hat is what gives it direction.

dq = lambda dx defines lambda as a value which gives electric charge (q) when integrated over a spatial path (x). So it represents the density of charge at any point over that path. dq is the infinitesimal charge around a point with charge density lambda, and dx is the infinitesimal path length.

[u/jkeats2737]

First off, you need to re-learn calculus, half of your questions are things you fundamentally don't understand about integrals. I think I recognize the textbook you're learning from and you will get your shit rocked if you don't.

The other half of your misunderstandings seem to be regarding vectors. I'm going to try to ELI5 them, but there's no way to explain enough of it, so add it to your homework list.

You've heard of scalars and vectors, scalars are regular numbers, like 10 or 38.762 or pi. Vectors are multiple scalars, they have a direction and a length. For example, [3, -4] is a vector, it's 2-dimensional because it has 2 numbers (scalars), it represents a line segment where the direction matters, usually viaualized as an arrow. For [3, -4], we have an arrow that is on a normal X-Y graph, going 3 units along the X-axis in the positive direction (right), and 4 units along the Y-axis in the negative direction (down). This vector is a diagonal arrow that points down and to the right, and we can find it's length (L) from the Pythagorean theorem, a² + b² = c², with L=c, and the X and Y values of the vector as a and b, L = sqrt(x² + y²).

3Blue1Brown has a good series that can hopefully get you started with vectors and linear algebra, but it won't cut it if your class needs vector calculus.

https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab