Just looked at the table of contents / some sections..... and wow. Literally a perfect match (more or less, about as close as I could hope) step by step to my course outline. Same style and cheap too. Perfect suggestion and supplement. Thank you for pointing me towards it, dover always has gems.
So the course I'm taking doesn't have a textbook requirement just lecture notes as the study material. While these are sufficient I would like to supplement with an outside reference that is a bit more in depth / explanatory.
It's your typical undergrad real analysis course covering:
The least...
I'm taking an abstract algebra course that uses Hungerford's "An Introduction to Abstract Algebra" 3rd Ed. And while I feel like I'm following the material sufficiently and can do most of the proofs it's hard to learn and practice the material without a solutions guide. How am I supposed to know...
In my calculus textbook (section on vector calc) it is showing that the gravitational field is conservative. I followed fine except for the first part, defining the scalar function f.
Showing the field is conservative went something like this:
f(x,y,z) = MM'G/\sqrt{x^2+y^2+z^2}...
I've put the problem statement below and worked it out. I typically don't post questions like this as they're a lot to go through, but I am wondering if I have worked the problem correctly as my book does not have the solution and I feel like I am not understand the material correctly.
1...
I think A student's guide to maxwell's equations is what I was looking for. Purcell has a great exposition as does griffiths, but I'm lacking at the problem solving and understanding applying the techniques. More or less going from thinking like a mathematician to a physicist, and that looks to...
I'm using purcell and I find the notation (CGS units) to be a bit confusing at times in formulas, but trying to struggle through it as I should go ahead and get exposed to different systems of units and I've had an undergraduate course on newtonian mechanics.
In purcell I don't find most of the...
Can anyone recommend a good book that deals with the mathematics of E&M? I've read through my calculus books and feel like I understand the material there and can solve the problems. However, when it comes to it's applications in electricity and magnetism I find that I have enormous difficulty...
I was missing the sign! That was it. I always get confused about whether to include signs or take the absolute value/magnitude. In columb's law we don't use the signs do we? Every time I've tried to use negatives in coulumbs law it came out wrong, or maybe I'm just doing it wrong. That's why I...
Homework Statement
A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
I'm not sure what you mean? I'm very bad at using symmetry doing these types of problems typically takes me ages as I can't identify the symmetry / relations correctly in square arrays of charge etc. Could you explain what you mean?
I didnt understand where the Q went until I reworked it and yes you're right. Is the below correct? It gives me the correct answer but as far as best way to solve technique etc goes not sure its close to good.
My notation could probably use some work... I realize I could have forgotten about...
Homework Statement
Consider the figure below, we need to find the charge on Q_0, both charges Q are negative. It is given that the net charge on Q_A is zero.
The figure of the problem is attached.
The Attempt at a Solution
I understand how to get the solution except for one part. I'm just...
Couldn't solve the derivative for b. I think I messed the derivative up I was getting high powers of b that couldnt be solved.
Sample of what I tried to solve...
d/db [b/(9+b^2)^{3/2}] \Rightarrow [3b(9 + b^2)^{1/2} - (9 + b^2)^{3/2}]/(9 + b^2)^3
After that it turned into a mess trying...
I dont understand? Q is restricted on the y-axis at a height of a = 3m the charge q is arbitrary at a location b. The first part of the problem is to find the value b at which the x-component of the force between the two charges is at it's miniumum which would be at b = 0. To find it's maximum...
Here's the picture of the figure, where a = 3m in this specific case. I guess I should have also stated that the b in the numerator and the 3/2 power came from the cosine to be more correct in terminology?
A charge Q is placed at a distance a = 3m and a charge q is placed at a distance b
For what value(s) of b is the x-component of the force maximized?
I know to maximize the force we need to maximize F_Qq = k Qq b/(3^2 + b^2)^{3/2}.
To do this we need to set the first derivative to zero and...
I think I messed up a little bit. The diagonal will be the side length, a, times square root of three.
I only need one face so I just need to multiply the result by 1/\sqrt 3. So, the result would be
F_Q = 4[1/4\pi \epsilon_o * q^2/r^2 ] * 1\sqrt 3
In the way I worked it I placed the...
Homework Statement
Four charges of 2*10^-7 are placed on the corners of one face of a cube of 15 cm. A charge of -2 * 10^-7 C is placed at the center of the cube. What is the force on the charge at the center of the cube?
Homework Equations
F = k q_1*q_2/r^2
The Attempt at a Solution...
Ah fair point forgot about those being strictly on the x-axis, so need to fix that then resolve into E_x and E_y for the respective terms and then take the square root of those squared for the magnitude.
The missing term is the -5q charge, yes? So it should be
E=k[−2q/(\sqrt2 * d)+q/(\sqrt 2 * d) + 2(5q/(\sqrt 2 * d))= k[9q / (\sqrt 2 * d)]
Also, changed q^2 to q since this is the electric field not force... silly mistake, and the bottom term should be \sqrt 2 * d instead of d^2?
This is...
Homework Statement
Find the magnitude and direction of net electric field at the center of the square array of charges. Find E_x and E_y
The square array of charges http://postimg.org/image/4gf94ymmf/
The Attempt at a Solution
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My attempt at drawing in the force vectors...
Can someone walk me through calculating the final step in this problem.
Problem statement:
If the charge q is produced by adding electrons to the mass, by how much will the mass be changed?
It was calculated that the charge q is 2.374 * 10^-7 C which is correct and I know that we need to...
Homework Statement
The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...
Have a quick question about taylor series. We covered taylor series somewhat in class, but there was a complete lack of explanation and our calculus book literally covers the topic in a single page.
I understand the idea of a taylor series and how its related to a power series, but what I don't...
Thanks for the detailed reply. Talked to a few different people today and that was pretty much the same conclusion we all came to that there would really be no graph theory applications. The only thing that I may be apply to apply is machine learning to possibly predict locations of where new...