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Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ then brought in contact with $C$ and finally removed away from both. The new force of repulsion bet... |
I just read that there was a machine to simulate economic processes using the flow of water (https://en.wikipedia.org/wiki/MONIAC) since some equations in economics are similar to the equations in fluid mechanics.
What are these equations or the concepts shared?
Are there other equations that share the similarity in ... |
In a paper which deals with the spectra of radio frequency cosmic events, the word “spectral turnover” is used. What is “spectral turnover”?
|
It is said in Lie Algebras in Particle Physics 2ed - From Isospin to Unified Theories (Georgi, 1999) p.285, Georgi said that
$\rm SO(10)$ grand unified model restores the parity symmetry that was lost completely in $\rm SU(5)$ model.
However, it seems to me that the spinor representation 16 alone in $\rm SO(10)$ mode... |
Einstein’s relativity rejects the notion of a universal ‘now’ moment. It underlines how the concept of ‘now’ is compromised due to time passing at differing rates in differing frames of reference, depending on such things as local gravitation or the acceleration of a body at high speed. Some other reasons I have seen e... |
Let's say an object of mass 10 kg is fired from a cart of mass 90 kg. The object and the cart, of total mass 100 kg were initially moving together with a speed of 10 m/s. Then, the object is fired by some means from the cart such that it's velocity increases to 15 m/s (w.r.t ground), in the same direction. Finding the ... |
If A and B are two commuting observables, and the observable A is first measured on an arbitrary state, and then B is measured on the resultant state, what is the variance in the last observation?
|
Consider a young's double slit set-up in water. Consider a point $p$ on the screen , such that $S_{2}P-S_{1}{P}=s$.
Then , Wave equation for wave from $S_{1}$ at point P: $Asin(2\pi/\lambda(x) -\omega t)$, and for the wave through $S_{2}$: $Asin(2\pi/\lambda(x+s) -\omega t)$=$Asin(2\pi/\lambda(x) -\omega t+ 2\pi/\lambd... |
I read that we get between 500 and 32k bits per second when sending data from Mars to Earth. Apparently it's substantially higher between Moon and Earth. What are the reasons? Please explain the relationship between frequency band used and range and bandwidth (if there is any) and perhaps the term bandwidth in general.... |
When we quantize a EM field with appropriate boundary conditions (say in a waveguide/cavity) we get modes denoted by the $\vec{k}$ and we know that $\omega = c|\vec{k}|$ so do modes represent different frequencies of the EM wave ($\omega_k$) and higher modes mean higher frequencies?
Also Fock states $|n\rangle$ are pho... |
In Chapter 9 in Quantum Field Theory written by Srednicki.
This chapter discusses why $Z_{i}=1+O(g^{2})$ and $Y=O(g)$, given specific values of $m$, $g$, and normalization conditions
$$\langle k|\phi(x)|0\rangle =e^{-ikx}\qquad\text{and}\qquad \langle 0|\phi(x)|0\rangle =0,\tag{9.2}$$
when considering an interacting qu... |
A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance
between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm
from the lens. The final image is
a) virtual and at a distance of 16 cm from the mirror
b) real and at a distance of 16 cm from the mirror
c) virtual ... |
As heat is supplied to an object, its lattice vibrates more. Thus average equilibrium position between ,say two adjacent atoms, increases with increase in temperature.
equilibrium=(r min - r max)/2
As average separation increases expansion occurs.
I was told that Ionic bonds are strong and compact ,so lattice vi... |
I know this sounds absurd, but after doing a little research I found that it may be possible (not entirely, but that is why I am asking about this here). I have been reading up on antimatter and quantum mechanics and I stumbled across this article on the subject of "creating antimatter with lightning". All lightning is... |
I began reading Hawking's paper Particle Creation by Black Holes (1975, Commun. math. Phys 43, 199—220) but am a little confused by what he writes at the bottom of the second page. The idea is that there is some indeterminacy or uncertainty in the mode number operator $a_i a_i^\dagger$ in curved spacetime.
What Hawkin... |
( Apologies for such a vague question but I'm a math student )
How two moving photons interact at a distance ?
I need some basic and standard references for it .
|
Why does unitarity imply a branch cut in the $S$-matrix after $s > 4m^2$ where $s$ is the Mandlestam variable and $m$ is the mass of the particle? Assume identical particle scattering.
|
Suppose that the are of the plates is 6.35 m sq and height is negligible. Both the plates could be made to slide. In the initial case the whole apparatus was empty. Door 2 was in closed position and door 1 was open such that when the water from the top of the tunnel was poured no water could leak from the door 2 side.... |
This is more of a conceptual question. Normally a conservation law will look something like
$$\frac{\partial j}{\partial t}+\frac{\partial F}{\partial x}=0\tag{1}$$
where $x$ is typically a real-valued coordinate, or even $\nabla$ if we have a space with a few dimensions in it. It's then pretty easy to define an integr... |
The following problem is taken from Exercise 1.7 in David Morin's "Special Relativity: For the Enthusiastic Beginner":
A train and a tunnel both have proper length L. The train moves toward the tunnel at speed $v$. A bomb is located at the front of the train. The bomb is designed to explode when the front of the train... |
I have a somewhat general question. If I have two loops of conducting wire, and I pass current through one, is the induced emf on the other loop the same electromotive force that would have occurred in the first one if I passed the same current through the other one?
|
In Goldstein's classical mechanics the following passage is confusing me:
We therefore have as the condition for equilibrium of a system that the virtual work of the applied forces vanishes: $$\sum_i \textbf F_i^{(a)}\cdot \delta \textbf r_i=0 \tag{1.43}.$$ Equation (1.43) is often called the principle of virtual wor... |
Say there is a spherical shell with radius $R$ and width $h$. For a certain purpose, I wanted to divide this object into many "rings with holes". Signifying by $\theta$ the polar angle, we have annulus with radii of $R\sin\theta$ throughout the shell ($\theta$ ranging from $\pi$ to $0$). On the one hand, shouldn't the ... |
What is the physics explanation for why an object with a larger base is more "stable" or more able to "balance"? For example - two pyramids, one on its tip (less stable) VS one on its base (more stable).
Also, which area of physics deals with this issue of stability, and which textbooks or monographs are good readings ... |
When deriving the stefan boltzmann law from planks law. You may make a substitution (http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan2.html). This substitution will lead to a stray minus sign in the equation. The rest of the derivation seems to just ignore the minus sign. Is there a reason for this?
|
The characteristic equation is as follows:
$E^2-\hbar \omega E -\hbar^2\omega^2\alpha^2 = 0 $
The eigenvalues I get are $\frac{\hbar\omega(1\pm\sqrt{1+4\alpha^2})}{2}$, however, I am being told the solution is $E_{0}(\alpha) = \hbar\omega(1-\sqrt{1+\alpha^2})$ and $E_{1}(\alpha)=\hbar\omega(1+\sqrt{1+\alpha^2)}$
I can'... |
I am reading the introduction to the textbook The Quantum Theory of Light, third edition, by Louden. When discussing the photon, the author says the following:
The idea of the photon is most easily expressed for an electromagnetic field confined inside a closed optical resonator, or perfectly-reflecting cavity. The fi... |
I'm studying structural mechanics and I have been stuck on a thought.
I drew a very simple cantilever beam situation. If I make a fictional cut like in my fig.1, I will be in the situation of the second figure. Unfortunately I don't understand how stress can still exist "inside" the beam since we can clearly see that t... |
I just started studying field theory and general relativity, and when reading paper titles I often see the word decoupling coming up.
My intuition is that there must be a cross term involving some different fields in the lagrangian so they interact proportional to some constant and then to decouple you take the limit w... |
I've read in this paper (doi:10.1038/nature07871) that in the context of quantum mechanics, $\rm SU(2)$ symmetry leads to the conservation of spin polarization, or in other words invariance with respect to the rotation of the electron’s spin leads to such conservation. I'm very new to the subject, hence, my question is... |
I'm slightly confused about the placement of upper and lower indices for the transformation of a rank-2 contravariant tensor.
A contravariant rank-2 tensor transforms as $$M' = \Lambda M \Lambda^{T}$$.
In index notation, $\Lambda = \Lambda^{i}{}_{j}$ and $\Lambda^{T} = (\Lambda^{T})^{i}{}_{j}$. Therefore, I assumed the... |
Given the standard geodesic equation:
$$\frac{d^2 x^\mu}{d\lambda^2}+\Gamma ^\mu _{\sigma \rho}\frac{d x^\sigma}{d \lambda}\frac{d x^\rho}{d \lambda}=0$$
we want to apply it to the Schwarzschild metric; conceptually this simply means using the proper $\Gamma$ coefficients, but in practice this leads to a gargantuan cal... |
It is given in my textbook and one other book(that I got from the library) that:-
...The earth has a magnetic dipole of dipole moment about $8.0\times 10^{22} \mathbf{ J.T^{-1}}$
The book doesn't state how we know it and it uses the word 'assume' which confuses me a little bit. Internet doesn't seem to help. Sources ... |
If its number of particles of a particular type is not conserved then it has zero chemical potential. Photon number is not conserved. Hence, it has zero chemical potential. We also know that photons have zero rest mass. Does particle number nonconservation (therefore, zero chemical potential) logically follow from the ... |
$$O=\exp\left(x^TAx +x'^T B x'+x^TCx'+x'^TDx\right)$$
Where $x^T=(x_0,x_1,..,x_{n-1})$, $x'^T=(x'_0,x'_1,..,x'_{n-1})$ and $A,B,C,D$ are complex square $n\times n$ matrices. The column matrices x and x' consists of real entries. Also, $A^\dagger=B$ and $C\&D$ are Hermitian. I need to know a proper eigenfunction to solv... |
The current through a capacitor as a function of time is given by;
$$i(t)=C\cdot \frac{d}{dt}U(t)$$
When assuming that the capacitance $C$ does not vary with time.
But what if it does?
I don't know how to derive the equation above from Gauss's law, so here is instead my attempt at a "common-sense" kind of solution, I d... |
If the wing of an air plane is cuboidal in shape, and that the Earth's magnetic field $\bf{B}$ is uniform in the neighbouring volume of the plane, does that mean the induced emf over the entire 'block' of wing is zero due to
$$\Phi=\oint_S \mathbf{B \cdot \mathbf{n}}dS=0 \tag{1}$$
and hence $E=-\frac{d \Phi}{dt}=0$?
Th... |
the electricity produce by DC generator is sinusoidal. I think that it may works but the thing is why it isn't use in power plant as ac and DC current (produced by generator without smoothing) can be step-up or step-down
|
I've seen this question asked a few times on Stack Exchange, but I'm still quite confused why the following "contradiction" seems to arise.
By definition:
$(\Lambda^T)^{\mu}{}_{\nu} = \Lambda_{\nu}{}^{\mu}$
$\Lambda^T \eta \Lambda = \eta$, which is $\Lambda^{\rho}{}_{\mu} \eta_{\rho \sigma} \Lambda^{\sigma}{}_{\nu} = ... |
A previous post (What Is Energy? Where did it come from?) defines work qualitatively as "a process in which energy is transformed from one form to another form". And mathematically, work is defined as:
$$\Delta KE=\int_{C} \vec{F}\cdot\mathrm d\vec{r}$$
But if you imagine lifting up a rock from the ground at constant s... |
One can calculate the Reynolds number to determine whether or not flow is turbulent or not inside a pipe with circulating water. The formula is:
$Re = \frac{\rho VD}{\mu}$
Let's say one gets $Re = 10,000$. This means that the flow is turbulent (so $Re >4000$, according to some sources). Now, if one looks at the Moody C... |
While reading books on nonlinear optics, I often come across concepts such as second-order susceptibility which is not covered in undergraduate E&M books like Griffiths. Are there any good E&M books that will cover such topics?
|
The Problem
Consider the given arrangement:
Point $P$ is equidistant from $S_1$ and $S_2$ .The glass slab in air has refractive index $\mu_{2}$, and the one in water($\mu_{1}$) has refractive index $\mu_{3}$. We need to find the relation between $\mu_{2}$ and $\mu_{3}$ such that $P$ is the central maxima. Both glass ... |
I am working on an internet-of-things gadget that connects to a home plumbing system. It needs a small amount of energy in order to run its circuitboard. So, how should we power this device. One option would be to use replaceable batteries or a power plug. But, I thought a more elegant solution would be to use a turbin... |
I'm working with a pressure vessel that is cooled to a reasonably cool temperature. Since it is cooled at pressure when the air exits the pressurized system the gas expands and thus cools a great deal more according to the gas laws.
I was wondering if this (extremely) cold air can be bubbled up through water to cool th... |
I am having issues with the following physics practice problem related to magnetic field change per time.
Given the following circuit and magnetic field, assuming the loop has a radius of 10 cm and an EMF of 10V is measured, what is the rate of field changed per time?
Using Faraday's law we have:
$$\epsilon = -\frac{\... |
There is a cylindrical conductor of radius $R_0$ and length $l$. The resistivity $(\rho)$ varies as a function of $r$ the distance from the center of the conductor. $\rho(r)=\frac{a}{r^2}$ where $a$ is a positive constant. I have to find the resistance of the conductor per unit length.
What I have tried so far is that ... |
Suppose we Have an atom $A$ that can emit light with frequency $\mu_1,\mu_2,...$ and an atom $B$ that can emit light with frequency $\nu_1,\nu_2,...$.
Now suppose that we have a molecule $AB$ formed from these two atoms.
Does this molecule emit light with frequency $\mu_1,\mu_2,... \nu_1,\nu_2,...$ or can we have extr... |
"The centre of mass of a system of particles is the point that moves as though (1) all of the system's mass were concentrated there and (2) all external forces were applied there." (Resnick et al, p.215)
"The gravitational force on a body effectively acts at a single point, called the centre of gravity of the body." (R... |
I'm reading Weinberg's paper on "Dynamics at Infinite Momentum" in which he proves a claim about the type of Feynman diagram that contributes finitely to the perturbation series and the type that contributes 0 in the infinite momentum frame. However, I don't understand the differences between the following set of diagr... |
The way I see it:
Assuming space is a perfect vacuum, a satellite should stay in circular orbit with CONSTANT RADIUS around earth forever but I think the radius should gradually decrease for the following reason. Are my thoughts wrong?
A satellite in circular orbit has a tangential velocity which earth people have prov... |
I've read every thread on StackExchange (and Quora and reddit...) that I can find about a physical intuition for the phase in the quantum wave function, and I still Just. Don't. Get. It. (Yes, I've seen this thread--didn't help!)
As a jumping off point, I've been watching this terrific visualization of the quantum wave... |
Background Info
I'm just starting to look into tensor analysis and general relativity. I have taken college level courses on Newtonian mechanics, electromagnetism, and special relativity that roughly follow the Feynman Lectures on Physics.
This Physics Stack Exchange answer states that
[spacetime] curvature allows and... |
Is it possible to have a sound wave with frequency so high that it causes permanent displacement of matter (the frequency is greater than the elasticity of the medium, so the medium is unable to return to original position)
If this is possible, what frequency would this occur at?
|
I haven't seen any literature on the difference between erasing the photon's which-slit information vs just hiding it forever. Erasing quantum-information is effectively just a perpetual quarantine from the universe. A perpetual quarantine sounds hard to do though since mankind would need to exist until the very moment... |
I remember reading a work stating that in the presence of a gravitational field, vacuum magnetic permeability and electric permittivity can change with distance $r$ to the center of said field.
This implies that the speed of light depends on $r$.
How does this fit with our measurements of $c$ since we are immersed in a... |
I have recently ran into an observation which broke my mental schemes, using the Sky Map mobile application.
For an introduction before my actual issue, I should state my understanding that, since the Sun is so far away from us, then all rays casted along any huge area (not involving an actual significant Earth angular... |
I am having trouble unpacking the following argument from page 72 of Goldstein's classical mechanics book.
We now restrict ourselves to conservative central forces, where the potential is V(r), a function of r only, so that the force is always along r. By the results of the preceding section, we need only consider the... |
In SR, there are a couple of paradoxes such as the bug-rivet paradox that require us to take into account a finite speed of impulse.
Suppose I have a rod at rest, and I yank one end to some speed. I know that there has to be a period of time where the other end stays stationary until a signal arrives.
It may help to im... |
My physics teacher has told me that if we have an elliptic orbit under consideration, we can consider it equivalent to a circular orbit of radius equal to that of the semi-major axis of the ellipse.
Why can we do it? Is there an intuitive way to think about it? How can we prove it mathematically?
|
If somebody wants to measure surface error of for example concave spherical surface - in most of the optical companies around the world Fizeau interferometer will be used, with relatively large, high-precision (and expensive) reference optics (transmission sphere, which will include reference surface).
Why very few are... |
Just came across magnetic field inside a solenoid and amperes law. Amperes law says that dot product of magnetic field and distance from current would give us the $\mu_p$ times the current enclosed. If we put an amperes loop inside a solenoid, would the magnetic field be zero as the current enclosed is zero?
|
I'm certain some of this relies on arbitrary choice, for even in Euclidean 3-space, there is no a priori preferred choice of left versus right hand coordinates. In fact according to Einstein:
There are thus two kinds of Cartesian systems which are designated as
"right-handed" and "left-handed" systems. The difference... |
My textbook says:
"In multiplication or division, the final
result should retain as many significant
figures as are there in the original number
with the least significant figures."
but it also says $6*(7.203)**2$ has four significant figures. Shouldn't it be one, considering the above rule?
|
In addition to total energy, which components of the angular momentum $(\mathbf{L}_x,\mathbf{L}_y,\mathbf{L}_z)$ are conserved in the presence of an external potential field $V(x,y,z)$? I've learnt that it is usually the $\mathbf{L}z$, but how should I prove it? There seems no way to find a relation between $V$ and $\m... |
From the ideal gas law, we are aware that PV = nRT, which seems to suggest a direct relationship between pressure and temperature, or that as temperature increases, pressure increases.
In my geography book, however, it is written that "The equator receives direct rays of the Sun, this causes the temperature to rise, he... |
Even though the magnetic field is a non conservative field, the potential energy of a magnetic dipole (current-carrying log or bar magnet) is defined in a magnetic field. How can this be possible? Please explain.
From what I have learned from reading other answers, the magnetic field, in some cases, behaves like a cons... |
The speed of light in vacuum is a universal constant and important in several branches of Physics. Even the constancy of the speed of light is one of the two postulates of Special Relativity (SR). But my questions are:
Why does the speed of light assumes the particular value $3\times 10^8$ m/s and not any other differ... |
This is a little question that I have been wondering when I need to cut sand paper with scissors.
Sand paper can be used to sharpen knives etc. when applied parallel with the blade surface. Also it can be used to dull sharp edges when applied nonparallel with the blade surface.
My assumption is that it should dull the ... |
I am reading Cheng&Li's book "Gauge theory of elementary particle physics". In section 16.2, I am confused by some assumptions.
Suppose we have a $SU(2)$ gauge theory in $\mathbb{R}^4$
$$
S=\int d^4x Tr(F_{\mu \nu}F_{\mu \nu})\qquad F_{\mu \nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+[A_{\mu},A_{\nu}].
$$
For insta... |
Physics laws should not be changed under translations, so the Hamiltonian must commute with the generator of translations, which is the momentum operator, that is $[H,P]=0$. However we know that $H=H_{0}+V$, then clearly we must have $[V,P]=0$. But we also know $V$ does not necessary commute with $P$, then does this me... |
I have watched a few lectures and have heard in quite some places that free will is an important assumption in physics. For example Bell's theorem assumes that the two experimenters can freely choose in what direction they measure the spin of the entangled particles.
But otherwise, why is free will important? Does it h... |
I am trying to make a simulation of a counterweight trebuchet, with a sling and a hinged counter-weigh, using Newtonian physics, by solving a set of simultaneous equations at each time step, then using some differential solving method, Heun's method or RK-4, to find the new positions.
I have taken some of my analysis f... |
I am currently working on velocity waves in spherical geometries: I am considering a 1D many-particle system confined on a circle with a global drift leading to rotations, similar to this simulation of so called "phantom traffic jams": https://www.youtube.com/watch?v=Q78Kb4uLAdA
In this simulation you can clearly see v... |
I knw it sounds dumb, but here is my problem. I can clearly imagine why amplitude has nothing to do with wavelength in a transversal wave, as they are measured along different axes in a graph. But in longitudinal, as particles vibrate along direction of wave propagation, wont twice the amplitude equal the wavelength? I... |
I am struggling with this question. I want to determine whether the potential of a protein is conservative or not if its dielectric constant depends on the local density of the protein. My model only considers a Lennard-Jones potential and Coulomb potential.
Considering two fixed charge residues separated by a distance... |
If I am driving at night and fall asleep, and when I wake up I see a wall in front of me.
What should my instincts be :
Should I just apply brakes?
Or should I apply brakes and try to turn the car in a circular curvature?
Any other method to save my life and my car?
Any help is greatly appreciated.
|
A homogeneous sphere is uniformly heated (or cooled) while the boundary is kept at constant temperature.
How does its temperature evolve in time and how is it distributed spatially?
|
As you can see below, I'd like to know why the saturation is decreasing with the temperature while the absolute amount of water remains constantly.
The image is taken from a description of a transformer where the relative humidity in oil is decreasing with the temperature, so I'd be happy if an explanation could fit to... |
The Lorenz-Transformation of the EM-Tensor F is given by the equation
$$ F'^{\mu \nu} = \Lambda^{\mu}_{\ \ \rho} \Lambda^\nu_{\ \ \sigma} F^{\rho \sigma}$$
Then it says that this is equivalent to the matrix-equation
$$ F' = \Lambda \ F \ \Lambda^T $$
How can i see that one of the Lambda-matrices is the transposed of th... |
I'm reading this book.It says: Doubling the gauge pressure does not double the amount of air in the tank. But doubling the absolute pressure does.
I don't understand why...when : $\text{Absolute}\ P= \text{Gauge pressure}+ \text{atmospheric}\ P$ ?
Also why is pressure a scalar when it always perpendicular to the sur... |
I have some problems understanding the symmetry of spatial wave functions.
In my experimental physics course they tought us that in atoms the total wave function $\Psi_{tot}(\vec{r}_1,\vec{r}_2)=\Psi(\vec{r}_1,\vec{r}_2)\chi(S,M_s)$ has to be anti-symmetric under the exchange of two particles, because that's what the P... |
While reading "Four lectures on Poincaré gauge field theory" (available at RG) the authors present a relationship between a tetrad $e^i_{\;\gamma}$ (with Latin indices coordinates, Greek indices anholonomic) and a generator of a (local) Lorentz transformation $f_{\alpha\beta}$:
$$\left[f_{\alpha\beta},e^i_{\;\gamma}\ri... |
I'm studying special relativity.
A general Lorentz transformation is defined by $\Lambda^T\eta\Lambda=\eta$.
Now,
\begin{align}
\eta'^{\mu\nu} &= \Lambda^\mu_{\;\;\alpha}\Lambda^\nu_{\;\;\beta}\eta^{\alpha\beta}\\
&= (\Lambda\eta\Lambda^T)^{\mu\nu}
\end{align}
How does this equal $\eta^{\mu\nu}$? All we know is that $\... |
Say I have two atomic clocks, perfectly in sync, in the same location on the equator of the earth. I put one of them in a jet and fly it around the equator. When I land, the jet clock that went on the voyage is behind the land clock that did not.
The way I understand SR, there is no sense in saying that the jet clock ‘... |
Two questions, 2nd to be written separately concerns more difficult problem for motion of extended charge distributions. First:
Two point charges q1,q2. Determine motion of q1 using Newton's ODE. Force is q1*q2/r^2. I assume this gives velocity of q2 relative to q1? I assume this result has coordinate system attac... |
A block of mass m is launched op an incline with speed $u$ on a rough incline. If it reaches the top find the minimum value of $u$. (slant height $l$)
Ans- $u=\sqrt{2gl(\sin \theta+\mu \cos \theta)}$
Why am I not getting the same solution of the question using energy conservation (I get $u=\sqrt{2gl\sin\theta}$). If ... |
What I don't understand is that when we increase the value of potential why does the photocurrent reach a saturation point? Because when we increase the potential the velocity of the electrons increases so they reach the collector plate faster, that is the number of electrons reaching the collector plate increases in a... |
I'm a mathematician who's been struggling with the search of connections between physics theories and $C^*$-algebras. The most known connection I found was that the observables in quantum mechanics are equivalently described by the elements of the $C^*$-algebra of self-adjoint operators on a Hilbert space, a result kno... |
It is known that the electrons behave in magn. moment detectors experiments at 45 degrees non classically but quantum mechanically where the amount of spin up and spin down electrons in percentage is 85% to 15% instead 75% to 25%. Can this be explained by describing the electron spin axis and magnetic axis not being fu... |
A short-barrelled machine gun stands on horizontal ground. The gun fires bullets,
from ground level, at speed $ u $ continuously for a period of one second, but does
not fire outside of this interval.
During this time period, the angle of elevation of the barrel, $ \theta(t) $, decreases from $ \frac{\pi}{4} $ to $ \fr... |
$\quad$ Wasilewski's method (Or the method that could be seen in Dr Stone episode 9) consists of piece of iron being struck by a lightning, which then magnetises it. Let's say, we have a cylindrical piece of iron of length $d$ and radius $r$. Then we insulate the iron and wrap a copper wire of length $l$ and cross sect... |
I was reading some information about the constant of electromagnetism $\epsilon_0$ $[\frac{C^2}{N\cdot M^2}]$ and according to my understanding it is the amount how much electric field is permitted in the space (vacuum). I do not understand this idea so much and I would like for an example in real life when the $\epsi... |
In Goldstein, chapter three, third derivation, given as, Kepler's equation can be written as
${\rho} = e\sin({\omega}t + {\rho})$,
Now I have to prove that the first approximation to ${\rho}$ is ${\rho_1}$ given by
$$\tan({\rho_1}) = \frac{e\sin({\omega}t)}{1-e\cos({\omega}t)} $$
and also
$$\sin({\rho_2} - {\rho_1}) =... |
We know that $\text{density}= \frac{\text{mass}}{\text{volume}}$, and density of water is $1000\, \text{kg/m}^3$.
If I want to float a $100 \,\text{kg}$ metal block then using the above formula of density I get $\text{volume}= 100/ 1000 = 0.1\,\text{m}^3$
Now if the dimension of the block is $50 \,\text{cm }× 50 \,\tex... |
In Goldstein's classical mechanics (page 36) he introduces the basics of the calculus of variation and uses it to effectively the Euler-Lagrange equations. However, there is a step in which the $\delta$ notation is defined:
$$\delta y\equiv \left(\frac{\partial y}{\partial \alpha}\right)\text d\alpha,$$
in which $\alph... |
I know that, for example we have
$$\frac{\delta g^{jk}}{\delta g^{lm}}=\delta^{j}_{(l}\delta^{k}_{m)}.$$
This topic was discussed previously e.g. on Physicsforums.com and on Phys.SE.
So I was wondering, how can I compute
$\frac{\delta R^{j}_{klm}}{\delta R^{a}_{bcd}}$?
And in general, how can I compute this quantity fo... |
I read that according to classical wave theory, light is viewed as a wave whose intensity is continuously variable. And for this reason, it is unable to explain the photoelectric effect. My questions are:
What does "continuously variable" mean?
How does the intensity of light being continuously variable make it unabl... |
Can insulators like plastics be charged with the help of conduction? What happens when such materials are brought in contact with charged bodies that might be conductor or insulator?
|
Consider a complex scalar field with Lagrangian
$$\mathcal{L} = (\partial_{\mu} \bar{\phi})(\partial^{\mu} \phi) - V(\phi)$$
with potential
$$V(\phi) = \frac{1}{4}\lambda(\bar{\phi}\phi - \eta^2)^2$$
The model is invariant under global $U(1)$ phase transformations. The minima of the potential lie on the circle $|\phi| ... |
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