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    Magnetic Monopole (Magnetic Charge)

    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...
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    Integral of Electric Field is Zero

    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. Homework Statement 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...
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    Fractional Calculus and Residues

    According to Fractional Calculus, the power rule can be written as (dm/dzm) zn = n!/(n-m)! zn-m For example, (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). For...
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    Passive Circuit Elements

    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...
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    Curl of A

    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...
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    I don't understand why it's chiral. It's not like any of the phenyl

    I don't understand why it's chiral. It's not like any of the phenyl rings are stuck in a single resonance structure.
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    How do people become cracks?

    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...
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    Momentum Squared Operator

    Homework Statement 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. Homework Equations <p> = ∫ ψ*(ħ/i ∂/∂x)ψ dx The...
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    Simple Expectation Value Question

    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...
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    Dirac Notation

    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...
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    Orbits problem

    Homework Statement 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...
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    Blackbody Radiation

    Homework Statement What I don't understand is the second part, with the angles. The more I think about it, the less it makes sense. Homework Equations R = c/4 U The Attempt at a Solution Whenever I did a surface integral in...
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    Special Relativity (1-dimensional Lorentz Transformation)

    Homework Statement During class today, I was told that: x' = γ(x-vt) y' = y z' = z t' = γ[t-(v/c2)x], where γ=(1-v2/c2)-1/2 (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...
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    Existence and Uniqueness

    Homework Statement x/√(x2+y12)-(l-x)/√((l-x)2+y22)=0 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.) Homework Equations x√((l-x)2+y22)-(l-x)√(x2+y12)=0 x√((l-x)2+y22)+x√(x2+y12)=l√(x2+y12)...
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    Why is the H-field inside a magnet reversed?

    Homework Statement As the title states. Homework Equations B = μH outside B = -μH inside The Attempt at a Solution Derp.
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    Good Approximation to the Log Function

    Homework Statement 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. Homework Equations We start with loga(b) =...
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    Approximation comparison

    This isn't a coursework problem. I'm on winter break. Homework Statement 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)n = lim(x→0) [(1+x)1/x]xn = lim(x→0) exn This...
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    Vector Triple Product

    Homework Statement 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...
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    Magnetism Variables

    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...
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    Best Organic Chemistry Book?

    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...
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    Gauss' Law and charges

    Homework Statement 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...
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    Electrric Field equations

    Homework Statement 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. Homework Equations dE = 1/(4πε₀) dq /r2 The Attempt at a Solution Problem 1 Take the unit circle on the plane, for example. Find the...
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    Power Series for log z

    Homework Statement 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. Homework Equations [PLAIN] [Broken] Here is the expansion of log z around z=1. The Attempt at a...
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    Incorrect proof for lim sin(1/x) at x=0

    Homework Statement I need to know what's wrong with the following proof: Assume that [Broken] [Broken][/URL] exists. In other words: [Broken] (1) But: