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We can define a divergence-less current from any Killing vector field $\xi^a$ by
$$ J^a[\xi] = \xi_b R^{a b}$$
I would like to show that
\begin{equation}\star J = \mathrm{d}\star\mathrm{d} \xi.\end{equation}
Or at least that
$$\int_\Sigma \star J = \int_\Sigma \mathrm{d}\star\mathrm{d} \xi.$$
This leads to the famous... |
If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system?
I think I have a small misunderstanding of the interpretation because i... |
I am more than happy understanding how to find the equation for the electric field for a ring of charge along its centre axis (see Electric Field: Ring of Charge). But in every explanation I have seen they use the symmetry of the problem to cancel out one of the components. I understand why they do this, it makes the c... |
In my textbook, the author deduce the expression of the lagrangian $L(q_i(t), \dot q_i(t), t )$ of a free particle only using classical physical symmetries where the $q_i(t)$ are independent coordinates and the $\dot q_i(t)$ their derivatives by time.
To simplify let's just pretend $q_i(t) = x(t)$, and the lagrangian ... |
Unless I'm wrong, I know that if a photon strikes an electron at the right frequency, the electron jumps to a higher energy orbit, and then comes back to its stable energy state. While coming back, it releases a photon whose frequency is exactly the same as the initial photon that struck the electron.
Now my question i... |
I always see that the speed of light is a constant and never changes. But has this ever been measured?
Have they taken a stationary object and measured the speed of light coming from it in a vacuum and then also measured the speed of light coming from a moving object in the same direction as the direction of the light... |
Considering the QED Lagrangian we get a solution of the form $A^{\mu}$. This solution has four degrees of freedom (dof). With the weak Lorenz gauge we reduce it to two dof. With this condition we also solve the problem of negative energies in our Hamiltonian.
But I think that if Dirac had thought the same way after the... |
I've been trying to calculate the cross-section for the process $e^-e^+\rightarrow ZZ$ in unitary gauge with vanishing electron mass $m_e=0$. I've obtained the following:
I've only determined the cross-section starting from the value $\sqrt(s)=183 GeV$ since, in order for the process to occur, I need $s>4M^2_Z$, with ... |
If $\nabla · \mathbf E = \displaystyle\frac{\rho}{\epsilon_0}$ and $\nabla · \mathbf B = 0$ is valid only at $t = t_0$.
How to use the remaining two Maxwell's equations:
\begin{align}
\nabla \times \mathbf E &= - \frac{\partial \mathbf B }{\partial t}\\
\nabla \times \mathbf B &= \mu_0 \mathbf J +\mu_0 \epsilon_0 \frac... |
What limits the ability of a camera/telescope to zoom in on distant objects?
The question is twofold:
What zoom really is?
Firstly, I would like to gain clear understanding of what we mean by zoom and zooming in. It seems that in the case of a camera/telescope we mean something different from the case of a magnifying ... |
The Electric field at point P (for an electric slab) is given by $E_P=\frac{\sigma}{\epsilon_0}$, however, since $E$ inside the metallic slab is zero, the electric field at point P is contributed by only one of the surface (near surface). So the electric field at P should be $\frac{\sigma}{2\epsilon_0}$ and not $\frac... |
This question is about statistical mechanics:
Why does it make sense to postulate, that in thermal equilibrium all micro-states with fixed U within a micro-canonical ensemble are equally probable?
When I was a student, I focused mainly on the mathematical derivation, and it was clear for me, that this is the condition... |
Upon solving a question where I had to find the Electric Field $\vec{E}$ due to an infinitely large uniformly charged sheet of charge density ${\sigma}$ , I found that the Electric Field at a point near the surface is given by $\frac{\sigma}{2 {\epsilon}}$.
But Electric Field is property that is dependent on the dista... |
I'm reading Griffith's electrodynamics and in it he mentions in section 10.2.1 that news travel with the speed of light in electromagnetism. To my understanding the news he is talking about are the electromagnetic waves, which travel through space. Later in the example 10.4 he calculates the electric and magnetic field... |
While trying to find out if there is a rigorous justification for Wick rotating a QFT, I came across this other question (link below [1]) that mentions the Osterwalder-Schrader Theorem that gives a set of conditions under which Wick rotation is valid.
Now, my question is the following:
Are the theories in which we nor... |
So this question is really basic compared to some others on this website.
I was reading professor povey's perplexing problem, a book on physics problem solving. I came across a problem which is below.
A sewage worker is inside a large underground aqueduct (diameter > a man’s
height) of circular cross section, and so... |
A particle of mass m and charge -q enters a region between 2 charged plates initially moving along the x-axis with speed $v_x$ .The length of the plate is L and uniform electric field is maintained between plates. Show that the vertical deflection of the particle at the far edge of the plate is $\frac{qEL}{2m{v_x}^2}$... |
We have been given the following problem in our GR course. I have been able to develop part of it successfully, but at some point, I'm not sure if I'm doing it correctly;
Let $ξ$ be a Killing vector and $s$ be a unitary vector field proportional to $ξ$. Show that $[ξ,s] = 0$.
I'm using there is a scalar function $f$ su... |
When a water drop and a mercury drop are taken into two different but same kind of conical tubes, the water drop on its own tends to move towards the narrower end and the mercury drop tends to move towards the wider end, why? Why does this happen? How do we explain this phenomenon?
Following is a question based on the ... |
Let $r < R$, where $r$ is the distance to a point from the center of the sphere where we want to find electric field and $R$ is the radius of the sphere.
Why can we use $\oint_S \mathbf{E}\cdot\text d\mathbf{s}=q_{in}/\epsilon_0$ ($S$ is the surface of a Gaussian surface) when there are charges outside of the Gaussian ... |
During a calculation of the Renormalization constant of the ghosts in QCD I stumbled over the following question:
When I calculate the self-energy of the Faddeev-Popov ghosts in $SU(N)$ non-abelian gauge theory ($N=3$ => QCD), I get, after dimensional regularization, the following expression:
$$-i\Sigma(p^2)=\frac{iNg^... |
Suppose I consider a massless rod of several discrete masses with an external force being applied to one of the masses. Following the derivation here, the net torque on the system depends only on the external forces. Namely, the text states that all internal forces are along the rod and thus cancel when taking their re... |
I've been reading about viscoelastic models and using Excel to plot some of their characteristics. I'm particularly interested in their response to a constant strain rate which reverses periodically and goes into tension as well as compression.
I've read a number of texts that discuss the Boltzmann integral and a coupl... |
There are a lot of questions on this site about gravitational waves and time dilation, and some of the answers are contradictory.
I have read this question:
Do gravitational waves cause time dilatation?
where Tom Andersen says:
In other words, if there was a beam of gravity waves, and one person was in the waves, the ... |
Chemical potential of noninteracting bosons is known to be negative because the Bose-Einstein distribution $[e^{(\epsilon-\mu)/T}-1]^{-1}$ should be free of singularities. However, I don't fully understand how it is connected with the thermodynamic definition $\mu=\partial E/\partial N$ of chemical potential as the min... |
In the attached Quantum Field image we have the mode expansions (for a Dirac field), with annihilation operators (for both particle and antiparticle) attached to an exponential with a (-ikt) while the creation operators are attached to a positive (+ikt).
If we switch these so that the annihilation operators are attache... |
I understood that if the distance between the discrete rotational energy states are very small, the number of quantum states can be approached accurately using integration of the same formula. This is according to the Euler-Maclaurin formula explained on page 2-3 here. However, I keep deducing the opposite for the cumu... |
The property of a projectile make me think about those sine and cosine graphs I had learned in trigonometry class, which the distance between every two points on that parabola is the same but the intervals between the points are getting bigger and bigger in the $y$-axis. (I just thought this is interesting)
In the case... |
I was solving this problem:
I was asked to find the capacitance per unit length, which I did (in cgs units)
$$C=\frac{w}{4\pi h}$$
and to find the inductance per unit length
$$L=\frac{4\pi h}{c^{2}w}$$
I've noticed that the following holds
$$C=\frac{c^2}{L}$$
is there some special significance to this relation, or is... |
Let us assume there is an ideal gas in a thermally insulated vessel and it is free to expand into vacuum through a small hole in the vessel.Would the mass flow rate be a constant? What would be the equation of force on the small hole.Which energy gets converted into the kinetic energy of the molecules if we assume inte... |
I'm fine with certain simplifying assumptions being made, I currently only know high-school level physics (the simpler the better). Also, if anyone can explain the intuition behind formulae, I would appreciate it.
|
For all the particles we know, except for the quarks, so like muon, proton, tau, bosons, neutrino, gluon, Higgs boson ecc. ecc. Is the charge always $q=0,\pm 1$$e$? Does a particle with fractionary electron charge or like $q=2e$ exist? (Except quarks).
|
In the case of Magneto-statics (Only time independent B field), we may solve the B(r) field from current density j(r) using ampere's law. Alternatively, we may also solve the B field if I know the magnetic dipole moment density m(r), by superpositioning the dipole fields (3rd eqn on this wiki page). I have a feeling th... |
Until recently I believed that the transfer matrix method such as used in solving the 1D Ising model could be used to solve the thermodynamics of any system that is:
1D
Translationally invariant
Has only nearest-neighbor interactions (or any fixed finite range), and
Has finite local dimension.
Besides being used for ... |
I'm trying to verify that, using Schwarzschild metric and using Newton mechanics, the same velocity over time for an object that is fallen to a planet in straight line, until some amount of approximation.
My objective: use Schwarzschild metric to analyze some basic problem (free fallen object speed in this case) and ve... |
What's the difference between locally Lorentzian and locally euclidean? Was the former (Lorentzian) the hyperbolic surface restriction of the latter (Euclidean)?
|
I know that for a body to complete motion in a vertical circle, the initial velocity at the lowest point must be such that the tension at the highest point is zero, what if the velocity is greater than the said value and the tension at the highest point is not zero?
|
In hyperbolic spacetime, we have this formula describing the surface:
$$ds^2=-c^2dt^2+a^2(t)\frac{dr^2}{1-r^2}\tag 1$$
I'm leaving out the angular distances because I'm just interested in a line-of-sight measurement (e.g. distance to a supernova). This formula can be represented by the metric:
$$g_{\mu\nu}=\begin{bmat... |
For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ .
In the answers they state the following:
The combination of angular momenta $L_1 = L_2 = 1$ gives $L = 2$
(symmetric), $L = 1$ (antisymmetric) and $L = 0$ (symmetric). This must be combined with the spin wave function of opposite symmetry, ... |
We had a question over on History.SE about why "hobo"s used to carry bindles (as shown in this picture from around the beginning of the 20th Century)
I wrote up an answer based on what seemed to me to be a pretty clear physical advantage of using a lever to help with the effort of dealing with that weight all day.
H... |
When playing a brass instrument, on a given harmonic, you can bend the pitch above (to a higher pitch) and below (to a lower pitch) where it sounds the best (while staying on the same harmonic, with the same length of tubing, i.e not changing fingering if playing trumpet or lengthening the slide on a trombone). However... |
With the development of suitable mid-IR ultrafast sources to drive High Harmonic Generation (HHG), researchers have reported the development of high harmonic X-ray supercontinuum sources. But how can we determine whether the source is coherent and can be used as a laser?
|
At which point in time in the history of our universe was the observable universe exactly as big as the entire universe? Does the Hubble Deep field represent such a time? Does this question make sense or am I forgetting that the observable universe grows directly proportional to universal expansion?
|
I have been studying QFT from Timo Weigand’s lecture notes and in the chapter ‘Quantisation of spin-1 fields’, he describes the Feynman rules for QED and after some examples, there is subsection named ‘Non-linearities’, where it has been written that loop diagrams induce an interaction between the photons and as an exa... |
I think there should be two ways of writing the equation for the impulsive spherical wave
from an impulsive point source at the origin, say $\delta(t) \delta(r)$:
$$(4\pi ct)^{-1} \delta(r-ct) \tag{1}$$
$$(4\pi ct)^{-1} \delta(t-r/c) \tag{2}$$
But these are not the same. In (1) the Delta Function has dimension 1/[L] a... |
We know that secondary winding receives it's voltage kick due to the fact that changing magnetic flux creates a rotational electric field that does not care about the ferromagnetic core.
This creates current in the secondary coil which creates a rotational magnetic field which further energizes the primary core.
This c... |
A Killing horizon is defined as a null hypersurface generated by a Killing vector, which is then null at that surface. Some often cited examples come from the Kerr spacetime, where the Killing vector $\partial_t$ becomes null at the ergosphere; one can also take a linear combination of that with $\partial_\phi$, which ... |
My basic physics' knowledge is a little rusty. My apologies in advance. I know that the first derivative of position or displacement with respect to time is the instantaneous velocity. Suppose I have a distance calculated with
$$D = \sqrt{\Delta x^2 + \Delta y^2}$$
Does $\frac{dD}{dt}$ have an interpretation? For examp... |
In the question there is a central potential within a Hamiltonian, and I have to find the appropriate quantum numbers. They say that $j, m, s$, $\ell$ are the appropriate quantum numbers to describe this situation. Why are $m_\ell$ and $m_s$ not included here? And do $J^2$, $m_j$, $S^2$ and $L^2$ always commute with th... |
It's unclear to me why the following doesn't work when I calculate the $Q$ value for $\beta^-$ and $\beta^+$ decay. If we start with a parent nucleus $P_z$ with $Z$ electrons decaying through $\beta^-$ producing a daughter nucleus $D_{z+1}$ with $Z+1$ electrons:
$$Q = (P_z + Z*m_e) - (D_{Z+1} + (Z+1)*m_e + m_e).$$
Ass... |
Stephen Hawking giving a lecture describing how the universe would have arisen from his model (developed with James Hartle) or "no boundary" conditions, once said:
Unlike the black hole pair creation, one couldn't say that the de Sitter universe was created out of field energy in a preexisting space. Instead, it would... |
A particle moves on a gravitational potential produced by the distribution of mass on a sphere of radius R.
First I calculated the lagrangian:
$T=\frac{m}{2}(\dot{x}^{2}+\dot{y}^{2}+\dot{z}^{2})$
$V=-\frac{GM}{R}$
$L=T-V=\frac{m}{2}(\dot{x}^{2}+\dot{y}^{2}+\dot{z}^{2})+\frac{GM}{R}$
Next I used the general formula for ... |
I tried solving the following problem:
"A 62.0kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 12.0m and falls a total of 31m. Calculate the spring constant $k$ of the bungee cord."
I first tried to use the law of conservation of energy to solve the problem:
Gravitational... |
I'm trying to draw Feynman diagrams for 'The decay of the pseudoscalar meson $\phi = |s \bar{s}\rangle $ into these final states:
i) $\phi \rightarrow \pi^{+} \pi^{-},$ where $\pi^{+}=|u \bar{d}\rangle$ and $\pi^{-}=|d \bar{u}\rangle$
ii) $\phi \rightarrow \pi^{+} \pi^{-} \gamma$
'
but when I was reading up how to do t... |
While I perfectly know the true demonstration of Heisenberg uncertainty principle (from the full QM machinery), I'm looking for a very cheap heuristic way of getting
$$\Delta x \, \Delta p \ge h, \tag{1}$$
without getting into the semi-classical "Heisenberg microscope" experiment, or any wave packet superposition. I n... |
Reading this post, How can one say that if we subtract "TS" from "U" then what we get is free energy? I read that:
Strictly speaking, free energy is the difference in the value of the
potential in the non-equilibrium state and the equilibrium state.
Therefore, free energy is a function of two states: the initial
... |
I understand how to derive the formula for diffraction gratings as you just have to compare the light rays approaching at a maxima point. The formula for diffraction grating formula is shown below : $$d \sin{\theta} = mλ$$ where $d =$ distance between slits/slit separation
From my understanding, the double-slit formul... |
I'm studying Peskin & Schroeder's An Introduction to Quantum Field Theory, specifically the section about the quantization of the Glashow-Weinberg-Salam model of the electroweak gauge theory where they analyze the $e^+e^-\to W^+W^-$ reaction (section 21.2, page 750 in my edition).
They affirm, if I read that right, tha... |
If I have an infinite cylinder with radius $R$ and a surface density of current that varies with time, I can use ampere's law to calculate the magnetic field. My question is why is possible to ignore the displacement current when calculating the magnetic field, in this case?
|
Can we use gauss law to prove that field in a cavity of charged conductor of any shape is zero?? If so how as the shape may lack symmetry? If not how can we prove the field to be zero? I know that the charge resides on the surface of conductor but I am not satisfied by the reasoning that since charge enclosed is zero f... |
A vertical thermally insulated cylinder of volume $V$ contains $n$ moles of an ideal monoatomic gas under a weightless piston. A load of weight $W$ is placed on the piston as a result of which the piston is displaced by a distance $h$. Determine the final temperature of the gas. Take area of cross section as $A$ and a... |
Why in cooling systems such as chilled water network and $\mathrm{AHU}$, the pipes network is indicted by pressure gauge instead of measure of flow
As the heat transfer equation $mC_{p}T$
The heat transfer is related to mass flow rate not pressure to make sure the process is working efficiently
|
If perpetual motion exists in atoms or its parts then why can it not exist with a collection of atoms? or can it? What exactly prohibits or where does the perpetual line physically stop? Can atoms be aligned to create a tiny vibration within a mass of atoms?
I've done much study on magnetized atomic perpetual motion. I... |
A $4F$-configuration is usually utilized for imaging with $2$ lenses. An object is placed in the focus of the first lens ($f_{1}$), then the second lens is located at a distance $f_{1}+f_{2}$ from the first, where $f_{2}$ is the focal length of the second lens. Finally, an image is formed in the focal plane of the seco... |
As I was learning semiconductor physics I learned that holes are deficiency of electrons.I also learned that the electrons from the n type material combine with the holes in p type and the electrons move along through these holes and conducts electricity in forward bias.
My doubt is that inspite of having higher energy... |
I don't understand the step under the red arrow. I'm assuming that the blue line isn't the ocean floor, for we're assuming "deep waters". I happened upon this picture on Reddit.
After you "exhale and sink" and "crouch", why will you necessarily bounce?
What depth best befits the "Crouch and bounce"?
|
Let's say that a concave lens $A$ has a focal length of $-10$ $cm$ and another concave lens $B$ has a focal length of $-20$ $cm$ and we need to compare their powers.
We know that :
$$P(D) = \dfrac{1}{f(m)}$$
Here, $P(D)$ means the power of the lens in dioptres (D) and $f(m)$ means the focal length of the lens in metres... |
The image formation by convex lens is due to retraction. The rays bend and hence appear the come from a different point rather than an object, which is called an image.
In the image attached below, the refracted rays should only be visible to an observer to the right of the lens.
But how are we able to watch the ima... |
I have a capacitor with stacked dielectrics where $d_1 =10^{-3} \ m$ , $\varepsilon_{1} = 7$ and $d_2 =0.5 \cdot 10^{-3} \ m$ , $\varepsilon_{2} = 2$ and $V = 500V$. How would I go about calculating the electric field intensity in each dielectric?
I know that I can treat the capacitor as 2 capacitors connected in serie... |
I am trying to lift a 10kg weight using 1kg weight as shown in diagram.
block A is 1kg and block B is 10kg will the lighter block be able to lift the heavier block. Also what will bw the height by which the heavier block will be lift.
is it possible and if yes what will be the height by which weight can be lifted.
|
In All the Classical Mechanics problems I have come across so far, There's one thing that happens invariably: That the work done by tension is zero. Mostly, It simply happens because the (massless) string is in-extensible(And therefore, no displacement),And the tension in the string is the same.
However, consider:
A ... |
I've been reading about what happens when matter and antimatter collide, but have been unable to locate an explanation of how annihilation actually occurs.
I've now discovered that quarks and antiquarks may play a pivotal role in the annihilation process, though am unable to find further information.
Can someone pleas... |
I have two questions, the second one is related to the first one.
1.The first question is about direction of acceleration in SHM. Now, we all know that the acceleration in SHM is directed towards center of oscillation. My point is about writing the equation correctly.
Say I have a spring mass system in the vertical d... |
In Goldstein's Classical Mechanics book, he considered a system of particles and looked at the conservative internal force between particle $i$ and particle $j$ that satisfy the strong law of action and reaction.
He wrote the potential function for this internal force as
$$V_{ij}=V_{ij}(|\vec{r_i}-\vec{r_j}|) .$$
He ... |
I was reading that the Apollo missions left a laser reflector (Mirror) on the moon for scientific use. Having read some of the controversy here and elsewhere about lasers being affected by refraction etc, I was wondering how a laser beam fired from Earth could find and successfully reach such a mirror?
|
I've done potential steps where V > E0 and V < E0, but not where it's equal to 0. How would I go about answering this question? Any help is appreciated.
See below.
|
Why is liquid surface tension written in units of mN/m, or milliNewtons per meter?
The related concept of surface energy for solids uses units of milliJoules per square meter.
|
In his original work Clausius defines the entropy from his equality $\oint \frac{\delta Q}{T}=0$, which holds for a reversible cyclic process. As it means the integral $\int \frac{\delta Q}{T}$ over a reversible process depends only on the endpoints, it follows a state function $S$ may be found such that the integral e... |
I learnt that for an uncharged capacitor of capacitance $C$ connected with battery voltage $V$, the energy stored by capacitor is equal to $\frac{1}{2}CV^2$. But in this example for the capacitor connected in parallel with the circuit on the right, will it get the same energy as the other capacitor connected on the l... |
In the book "Physical Chemistry An Advanced Treatsie VIIIA" Eyring, Henderson and Jost use the thermodynamic relation:
\begin{equation}
\left(\frac{\partial\rho}{\partial\mu}\right)=\rho\left(\frac{\partial\rho}{\partial P}\right)
\end{equation}
$\rho$ is the number density ($N/V$), $\mu$ is the chemical potential and ... |
So, one of my homework problems reads
A particle is trapped in an infinitely deep square well of width $a$, suddenly the walls are separated by infinite distance so that the particle becomes free. What is the probability that the particle has momentum between $p$ and $p + dp$?
I know that if the wavefunction of a par... |
Isham, in his Lecture on Quantum Theory, Chapter 7, Unitary Operators in Quantum Theory, Section 7.2.2 Displaced Observers and the Canonical Commutation Relations, mentions on page 137 (bottom) the following.
The final step is to identify the operator $\hat{d}_x$ with $\hat{p}_x/\hbar$, where $\hat{p}_x$ is the momen... |
The Schmidt Decomposition of a state $|\Psi_{AB}\rangle = \sum C_{ij}|i_A\rangle |j_B\rangle$ can be written in this form $|\Psi_{AB}\rangle = \sum \lambda_k|k_A\rangle |k_B\rangle$ where $\lambda_k$ are the Schmidt coefficints. I was reading a manuscrip provided online, written by an expert in this field, and he wrote... |
Let me start by saying I understand the Mathematics behind the twins paradox and how it is resolved. I understand that due to the acceleration of one twin, time from their subjective experience is slower and have done the Maths to verify it. Here is my problem: why is it that one twin is accelerating and the other isn'... |
I thought it would be so because the mass inside the earth would attract us however they would be at a larger distance than masses on the surface of the earth.
For example, consider having a tall building near the object. Would the effective force vector of the object be pointing into the center of the earth or deviate... |
As I was reading Jackson (3rd edition), On page 543 I see two different types of derivatives. they are given,
(11.76)
$$ {\partial^\alpha} {\equiv} \frac{\partial}{\partial x_\alpha} = (\frac{\partial}{\partial {x^0}}, -\nabla) $$
$$ {\partial_\alpha} {\equiv} \frac{\partial}{\partial x^\alpha} = (\frac{\partial}{\par... |
Consider the coherent state
$$ |\phi \rangle = \exp \left( \zeta \cdot \sum_\alpha \phi_{\alpha} a_{\alpha}^\dagger \right) | 0 \rangle.$$
For the case of bosons ($\zeta = +1$), the $\phi_\alpha$'s are $c$-numbers and the creation and annihilation operators satisfy some commutation relations. For the case of fermions (... |
How close would a supernova be to endanger the astronauts on the ISS?
Would Betelgeuse be close enough?
|
Some time ago, I started looking back at my notes from high school and now I have a question regarding the direction of the induction current I've been thinking about for days. It might be too easy for you experts, but here it goes anyway.
First, notice please that - whenever I refer to the direction of the induction c... |
Can a theory of everything solve the oldest problem of turbulence?
Can we have unified theory of universe without solving the problem of turbulence?
|
If under some generalized coordinates the force can be written as:
$$Q_j =-\frac{\partial U}{\partial q_j}+\frac{d}{dt}\left(\frac{\partial U}{\partial \dot{q}_j}\right).$$
Then can the force always be written in that form under any other generalized coordinates for that problem?
(If not then the potential about EM for... |
I'm putting together some charts and the time axis in one shows billions of years, the time axis in another shows millions of years. I've seen in various publications $my$ and $myr$ (also $ma$) for millions of years (ago). I've also seen $Gy$, $Ga$, $Gyr$ and $bya$ for billions of years.
I tried digging up an SI unit... |
Coulomb's Law is represented as $F = \frac{1}{4\pi\epsilon_{0}}\frac{q_1 q_2}{r^2}$ (in vacuum)
In any other medium , $F = \frac{1}{4\pi\epsilon_{0}\epsilon_r}\frac{q_1 q_2}{r^2}$
My doubt is that , is this $\epsilon_r$ the permitivity of the medium or the dielectric constant of the medium?
|
In Kerr-Newman metric it has stationary EM tensor Fab solution, with this solution E*B not equal to zero,and the charged particles can be accelerate along magnetic line. With charged particles pulled into BH, can BH hold the cahrge Q?
|
I am a beginner to QM and was studying about the Kronig Penney model and understood the derivation of the following equation,
$$ \cos(ka) = \frac{P}{\lambda a} \sin(\lambda a) + \cos(\lambda a)$$
where $ \lambda = \sqrt{\frac{2mE}{\hbar^2}}$ and $ k= \frac{2n\pi}{Na}$ where $'N'$ is the no.of lattices considered and $... |
I'm looking for books that explain/model vibration concepts such as multi degree of freedom vibrations from a mechanical vibrations standpoint (not waves). I'd prefer if it has proofs for most concepts and goes into the matter from a fundamental level. Multiple books covering different topics are fine.
|
Example: Let $m$ be a point mass that hangs at the equilibrium point $y_0$ on a spring fixed at the end. No damping force acts on the particle. Let $k$ be the spring constant.
If I want to calculate $y(t)$ I can use newton's second law to get: $m\cdot y''(t)=m\cdot g -k\cdot y$ or $y''(t)+\omega_0^2\cdot y=g$ with $\o... |
I know that mathematical general definition of wave in One dimension is $y(x,t)=f(x\pm vt)$.
Now I don't know that what this function $f$.for example $f$ can be $f:[-1,+1] \to \mathbb{R} : f(x)=x$ ?
|
I read Ben Franklin had it wrong by stating "current is the flow of positive charge". Right from the start Ben Franklin could have easily decided to say that current is the flow of negative charge.
So why is it that when J.J Thompson discovered the electron the physics community decided the correct elementary particle... |
Is there a difference between renormalization and renormalization group? In his book 'Scaling and Renormalization in Statistical Mechanics', John Cardy states the following about the term Renormalization Group:
"This terminology is rather unfortunate. The mathematical structure of the procedure, in the sense that it m... |
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