An electric charge produces a Coulomb electric field:
E = dqe r/r3
A current element produces a Biot-Savart magnetic field
B = i dl×r /r3
From what I understand, magnetic charges are inserted for the sake of making Maxwell's equations symmetric.
A magnetic charge is meant to produce a...
Hi everyone. This isn't a homework problem. Rather, I'm trying to understand how the δ term arises from the field of a dipole.
Greiner supplies the following one-line derivation, which is easy to follow I guess, but doesn't make logical sense to me. Specifically, I don't...
According to Fractional Calculus, the power rule can be written as
(dm/dzm) zn = n!/(n-m)! zn-m
(d1/2/dz1/2) z1/2 = (1/2)!/(1/2-1/2)! z0 = (1/2)√π
To find the residue of f(z) = f(z)/(z-z0)m at z→z0, the formula is Res(z→z0) f(z) = 1/(m-1)! dm-1/dzm-1 f(z).
The three circuit elements are capacitors, resistors, and inductors, which act in the following manner:
Capacitor: V = (1/C) q
Resistor: V = R dq/dt
Inductor: V = L d2q/dt2
Is it possible to build a passive device that acts like:
V = (const.) d3q/dt3
Google search has come up with...
Simple question. It came out of lecture, so it's not homework or anything. My professor said that the curl of a vector field is always perpendicular to itself. The example he gave is that the magnetic vector potential A is always perpendicular to the direction of the magnetic field B. (I haven't...
Recently, I came across a website of a guy that has had a physics education, but for whatever reason, he rejects it. He seems more like a troll than a legit crack. However, this got me wondering: how do people become so delusional as to dedicate hundreds of hours writing such crap? Do you think...
This problem is about the momentum squared operator. First, I state how I saw the derivation for the momentum operator. Then I state how I attempt to (and fail to) derive the momentum squared operator using the same methods.
<p> = ∫ ψ*(ħ/i ∂/∂x)ψ dx
I was told that given a probability distribution p(x) dx, the expected value for x is given by:
<x> = Ʃ xi P(xi) = ∫ x P(x) dx
This part makes sense to me. It was justified to me through the use of weighted averages. However, my teacher then made a hand-wavy move to generalize the above...
This isn't a homework problem, but it's so simple that it belongs here.
Can someone please explain to me bra and ket notation? I've been consulting various books and they are all so abstract. Yesterday, my professor told me that a ket |ψ> represents a column matrix and a bra <ψ| represents a...
This is a conceptual question. Does the Earth orbit the sun or does the sun orbit the Earth? I know this is silly of me to ask. After all, everyone learns at a young age the the Earth -obviously- orbits the sun.
We can represent the Earth orbiting the sun by defining the...
What I don't understand is the second part, with the angles. The more I think about it, the less it makes sense.
R = c/4 U
The Attempt at a Solution
Whenever I did a surface integral in...
During class today, I was told that:
x' = γ(x-vt)
y' = y
z' = z
t' = γ[t-(v/c2)x],
(This is just the standard Lorentz transformation.)
Then I was told that we could find dx/dt, the inertial velocity, by finding dx' and dt' and dividing...
How do I prove that the above equation has a solution for x in ℝ and that the solution is unique?
(y1, y2, and l are constants.)
So in my biology class, my professor wants us to use the Nernst equation without using calculators. I personally think this is stupid. However, I have no choice, so today, I tried coming up with approximations of the log function.
We start with loga(b) =...
This isn't a coursework problem. I'm on winter break.
A common approximation used in physics is:
(1+x)n ≈ 1+nx for small x
This implies that
lim(x→0) (1+x)n = lim(x→0) 1+nx
which is a true statement. However,
= lim(x→0) [(1+x)1/x]xn
= lim(x→0) exn
This isn't a coursework question. Rather, I'm asking for help on a geometric proof of the vector triple product. I find it strange and annoying that I can't find this proof anywhere online, because everyone just uses the messy expansion proof, and I hate that proof because...
This isn't really a homework problem or a problem that I can just figure out. I'm wondering why the letter B represents the magnetic field. Also, what does H represent?
(For example, F represents the "force" field, E represents the "electric" field, V represents the scalar voltage. I'm actually...
As the title states, what is the best book?
The book I'm using now is Vollhardt and Schore. I don't like it very much. The book is very spammy, if you know what I mean. I'd like a book that builds on previous facts. My current book just presents facts with little relation to previous topics...
Gauss' Law states:
∫∫ E.dS = ∫∫∫ div(E) dV = Qenc/ε₀
The proof is as follows (this is from Marsden's Vector Calculus 5e):
Let M be a elementary region in ℝ3. Then if (0,0,0) ∉ ∂M, we have:
∫∫∂M r.n/r3 dS
= 4π if (0,0,0) ∈ M
= 0 if (0,0,0) ∉ M
Construct a sphere of...
Given an arbitrary curve or surface with a total charge of Q, find the vector equation for the electric field at any point in space.
dE = 1/(4πε₀) dq /r2
The Attempt at a Solution
Take the unit circle on the plane, for example. Find the...
Does there exist a power series expansion of log z around z=0? If so, what is it? If not, demonstrate that it is impossible.
Here is the expansion of log z around z=1.
The Attempt at a...
I need to know what's wrong with the following proof:
Assume that http://img16.imageshack.us/img16/4839/eq1.gif [Broken] [Broken][/URL] exists. In other words:
http://img8.imageshack.us/img8/1856/eq2.gif [Broken] (1)