I’d like to find a function which has the level curves attached in the image, i.e. centered in the first quadrant (between 0 and 1) and with an elongated peak. Maybe some kind of a Gaussian surface, i.e. $f(x,y)=Ce^{-(x+y)^2/D}$. I've tried Desmos, but to no avail.
@schn that certainly looks like a Gaussian - try fiddling around with $f(x,y) = A \exp\left(- \left(\frac{(x-x_o)^2}{2\sigma_X^2} + \frac{(y-y_o)^2}{2\sigma_Y^2} \right)\right)$
A is the amplitude, $(x_o, y_o)$ is the center, while $\sigma_X$ and $\sigma_Y$ control the spreads
Hi @JohnRennie did you checked series capacitor problem?
Also I am confused with force direction of electric field and magnetic field. Does In EM wave direction of Force of Electric field and Magnetic Field is same???
Electric field Force F_electric direction in diagram plot perpendicular to the direction of change motion. And Magnetic field B plot perpendicular to electric field E. It means force of magnetic field F_magnetic = q (v x B) it shows force of magnetic field is perpendicular to both charge motion and magnetic field direction. Which becomes the exact same direction F_electric (direction) = F_magnetic (direction). Not magnitude only direction
Yes Your explanation is seems right. But in book numerical I got the result what I have written. Also reffred two different solution manuals both have same results.
In my opinion series join two capacitors have potential differences which lead to flow of charge until charge become same on each capacitor. Then new potential is established at which charge is same on each capacitor.
I think different potential is allowed in series join. V = V1 + V2, but different charge on each capacitor is not allowed. Due different charges on each capacitor charge flow from one greater charge capacitor to lower one. If wire has no resistance flow of charge is conserved Otherwise not (but calculation not showing conserved). In book we are taking an ideal conditions. I don't know the right explanation. Aaah... ;O
I just came to knew why Computer Science & Engineering is called Computer Science Engineering and not Computer Science & Engineering because & is not a valid character while naming files.
@undefined we don't really "prove" things in physics :P "Observing" what happens to an individual particle when a beam reflects off a mirror isn't really feasible
@ACuriousMind I'm trying to wrap my head around this for many months now. But sadly I still can not fully understand it. And I feel like every explanation I find is not detailed enough (or I simply don't understand them). But I can't get rid of the feeling that there is something missing
@undefined The "detailed" explanation would be that you have to compute the quantum mechanical interactions of the photons with the mirror surface and then find in some classical limit that it reproduces the simple classical reflection behaviour we observe for the beam
every physical explanation you get that somewhat comprehensible for a layperson is usually simplified to some extent, this is not unusual
the question which led me to the 'how does mirrors even work' is the question 'How does a reflected photon keep its entanglement?' (I know there are some questions with answers about this) but I feel like they are not satisfying and/or that something is missing.
but when I try to combine pieces from various answers from questions about this topic, I always feel like I dont understand it at all and/or that something is missing
like the sentence from Emilio 'each atom in the mirror will absorb and re-emit photons'. If the atoms absorb and re-emit the photon, why/how does it not lose an entanglement? How does this absorb and 'processing' in the atom really works?
for me it feels like I have a bunch of puzzle pieces in front of me but I can't put them together to reveal the beautiful whole picture
I was surprised to read this, anyone know exactly what it means? I thought the whole problem of qft was that 1. it can't be done fully non-perturbatively and 2. there are basically theorems that say perturbative qft doesn't even exist
@Charlie QFT is not defined by perturbative methods - you can write down non-perturbative definitions of e.g. what a scattering amplitude or the expectation value of some observable is. You can't really compute that, but you can write it down. Then you can do other stuff - often perturbation theory or lattice computations (which are not perturbative, juts approximative in a different way!) - to actually compute these things
Concretely, the asymptotic series over Feynman diagrams is a way to compute amplitudes, but it is not its definition
in string theory, a close analog to the series over Feynman diagrams, a sum over worldsheets, is taken as the definition of stringy ampltudes
i.e. it's not that we have some non-perturbative idea that we approximate via a perturbative series, string theory just takes this perturbation series as the amplitude, there's no approximation there
Many believe there "should" be some underlying non-perturbative theory (cf. "string field theory", "M-theory",...), but so far they've got nothing conclusive :P
$F_{Magnetic} = q ({v} \times \vec{B})$ it shows force of magnetic field is perpendicular to direction of both $\vec{v}$ & $\vec{B}$ due to cross product. Which is the direction of electric force.
@123 1. If you're talking about an electromagnetic wave again where electric and magnetic field are perpendicular, you should say so. How is BioPhysicist supposed to know that? 2. There is more than one perpendicular direction to a given vector unless you're in two dimensions.
(i.e. just because the magnetic force and the electric field are both perpendicular to the magnetic field, that doesn't mean they're parallel)
@BioPhysicist that's pretty cool - I suppose the general public doesn't get to hear as much of the mathematical modelling aspects of biology. Are there many BioPhysicists like yourself? (I don't know many people who enjoy both fields :D)
look at this link. $F_{Magnetic} = q (\vec{v} \times \vec{B})$ direction of propagation of EM wave is the direction of $\vec{v}$ and direction of $\vec{B}$ magnetic field is perpendicular to electric field. But $F_{Magnetic}$ is perpendicular to both $\vec{v}$ & $\vec{B}$ due to cross product.
So direction of magnetic force & direction of electric force become same. because direction of electric field and direction of electric force is parallel.
oh ok. Well I am in the physics department at my school, but there are 4 biophysics labs within that. Then there are some biophysics people over in the biology department too. I am unsure about numbers though
@schn to make it more egg shaped, you need to prefix the (x - x_o) term with a factor; to rotate it, you'll need to add in a $b(x - x_o)(y - y_o)$ cross term
@geocalc33 it is surprisingly hard to tell whether a metric is equivalent to another metric just by looking at it. The only reliable way to tell a metric is the same as the Minkowski metric is to compute the Riemann tensor and show it is zero.
@123 I don't know what you mean by that. Forces act on bodies, not waves. The magnetic force on a body with charge $q$ and velocity $v$ in a magnetic field $B$ is $qv\times B$.
whether that magnetic field belongs to an EM wave or comes from something else is completely irrelevant
@ACuriousMind i meant to say if Direction of magnetic force and electric force of EM wave is same it apply force on particle in same direction. How do we know it is due to electric force or magnetic force. This is the problem
@NiharKarve I've tried Geogebra and I can see it somehow being rotated when adding the cross term, but in WolframAlpha the level curves look a bit strange. Consider first adding a prefix to $(x-x_0)$.
Er, the cross term needs to be inside the exponential (sorry if I was a bit unclear) - like this: $f(x, y) = e^{a(x-x0)^2 + b(x-x0)(y-y0) + c(y-y0)^2}$
