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As I was reading Goldstein, there is the Hamiltonian $H$ such that,
$$\delta \int_{t1}^{t2} (p_i\dot q_i - H(q, p ,t)) dt = 0, \tag{9.7}$$ and Kamiltonian $K$,
$$\delta \int_{t1}^{t2} (p_i\dot q_i - K(Q, P ,t)) dt = 0. \tag{9.6}$$
This is ok.
Then,
$$\lambda(p_i\dot q_i - H) = P_i\dot Q_i - K + \frac{dF}{dt} \tag{9.8}$... |
I understand how to do transformations of four velocities, acceleration and so on under Lorentz boosts. However after all I have learned in special relativity I still don't know how just an ordinary particle's velocity changes due to an external force.
That is if I'm given a particle with some velocity and we apply a ... |
Following on from this specific diagram, I am not sure why this is possible via a gluon:
Why is $d\bar{d} \rightarrow s\bar{s}$ possible via a gluon?
The down quarks have a mass lower than the strange quarks, so how does the gluon change the down-antidown pair into a strange-antistrange pair?
This makes me wonder wh... |
If the fluid has zero viscosity, does that mean it is at rest? Would it be possible that the fluid is both at rest and has zero viscosity? Please explain.
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I understand that, to determine the spectrum radiated by a black body at a particular temperature (say a piece of perfectly black glowing coal), we can model the object as a cavity (with an infinitesimal hole where the object is) that contains nothing but electromagnetic waves. Even though there is nothing in the cavit... |
If I know the height of the object and how much liquid is above it, why is the formula for calculating the pressure acting on the bottom of the object still height times density times the gravitational constant?
As far as I can make sense of it if the object is in the liquid then the forces acting on the bottom of the... |
The star Alpha Centauri is 4 light years from Earth. For an astronaut travelling at $c/2$ from
Earth to Alpha Centauri. So, this apparently means
The colour of a distant star perpendicular to the direction of travel is different than as
seen from Earth due to time dilation.
I don't understand this, please help
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Using the hall effect calculations how can we determine a semiconductor is p type or n type
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Is there an intuitive approach to understand gyroscopic motion based on Newton's laws without passing through angular momentum conservation?
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So I learned about the Dirac equation which describes a relativistic free particle with spin $\frac{1}{2}$. I get the mathematics but what i can't find nowhere:
What are the observables of this theory?
Surely since the aim is to describe a relativistic particle there has to be some form of obtaining the probability... |
A planar diagram is defined as being one of the leading diagrams for $N \to \infty$ (large $N$ expansion), and, as I understand it, it should have the lowest genus when compared to a non-planar diagram. It is of course very useful to be able to distinguish planar from non-planar just by looking at the diagram without h... |
For the canonical commutation relation $[\hat{x},\hat{p}]=i\hbar\hat{\mathbb{1}}$ to be true, the operators $\hat{x}$ and $\hat{p}$ are to be described by infinite dimensional matrices only, cf. e.g. this Phys.SE post. Consequently other operators representing physical quantities must also be of infinite dimension (whe... |
I want to understand why exactly resistors or materials with high resistivity difficult the flow of current. If I'm not mistaken, there are not many free electrons in this materials to move and contribute to the current. But now comes my question, why can't the free electrons that come from conductors (for example a wi... |
https://m.youtube.com/watch?v=HneFM-BvZj4 (excerpt from the 2014 World Science Festival Program Dear Albert. Actor Alan Alda and physicist Brian Greene discuss Einstein's relationship with the "unruly child" of quantum mechanics, and how the famed physicist came up with the Special Theory of Relativity).
From about 9... |
A textbook mentions:
A bulb has a solid filament that is heated. Energy levels in solids overlap, so all energy changes for the electrons are allowed. This means the electrons can emit photons with any energy, producing a continious spectrum when a solid is heated.
I don't understand what it means by 'overlap of ene... |
I'm currently preparing for my Physics II exam about electromagnetism so I'm trying to go thorugh some problems.
I came across one that I'm just not able to solve and I thought that maybe someone could lead me in the right direction to solve it.
The problem is:
An infinite long dielectric rod (dielectric constant $\e... |
I found out recently that computer screens are only able to display a subset of all the colors visible to the human eye. Naturally one of my first questions was what do the other colors look like, but this is one of the few questions that I cannot Google. I have been able to find a few objects around my house that I'm ... |
In the mit ocw lecture by Prof. Lewin on EMI, He quotes a few statements from here to couple of seconds of the lecture.
I am confused why the sign of $L\frac{dI}{dt}$ changes, when we go around and evaluate the closed loop integral in the opposite direction of the current.
By faraday's law , we have
$$\oint_{+\partia... |
Why is the surface of the iced tea in the pictures below so uneven?
To give more details, today I tried (and failed) making iced tea.
I placed a cup of hot water, after removing the tea bag, in my refrigerator's freezer (so that it will cool quickly).
Naturally, I forgot all about it.
A few hours later I opened up the ... |
As a mathematician, holomorphicity is an extremely good property that provides rigidity, finite dimensionality, algebraicity. etc to whatever theory that's considered. I'm curious about why (anti-)holomorphicity is considered in physics.
As an example, apparently holomorphic representations of $SL(2,\mathbb{C})$ apply... |
Sunlight reflecting off my glasses seem to disperse into these distinct red and blue bands. The glasses are acting as some sort of a prism to split the light. The glasses do have some reflective coating (if that helps).
Any thoughts on what might be causing these?
|
I was reading Many Particle Physics by G. Mahan and they calculated the Green's function for electron-phonon interaction using Feynman's Diagram. It was written that Green's function contribution by diagram (c), (d) and (e) will be zero because they exist only if $q_1$ is zero. The reason they gave was that a phonon wi... |
I'm trying to understand this concept for a few days now to no avail. Consider some polarized ball with radius $R$:
The polarization is nonuniform, for the sake of example say $\vec{P} = (R-r) \hat{z}$ becuase I want it to vanish at the shell. I drew some of it on the ball.
I can't seem to figure out the electric fie... |
The rotational kinetic energy for a body that is rolling is is $\boldsymbol{\frac{1}{2}Iω^2}$ (where $I$ is moment of inertia about its centre of mass) and the translational kinetic energy is $\boldsymbol{\frac{1}{2}mv^2}$ for a rolling body..where $v$ is speed of its centre of mass for an inertial observer
If we add ... |
When I throw a rock in the water, why does only a small circular ring around the rock rises instead of the whole water body, and why does it fall outwards and not inwards or why fall out in any direction instead of just going back down like ball which after getting thrown up falls back to its initial position?
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Could be detected by infrared radiation?
|
This question is with reference to a problem in "Problems in General Physics by IE IRODOV" (Particularly problem 1.42 ).
The original problem is :
A particle moves along the plane trajectory $y(x)$ with velocity $v$ whose modulus is constant. Find the acceleration of the particle at the point $x=0$ and the curvature r... |
As we all know that Faraday's law states that the EMF is also given by the rate of change of the magnetic flux:
$$\text{emf} = -N \frac{d\Phi}{dt}$$
So if we are applying a time-varying magnetic field(let $dB/dt =$ constant) on a stationary conducting coil then induced electric field across the coil work as a driving f... |
This may be a fairly stupid question, but I will ask it anyway.
I am currently trying to calculate the steam pressures required to hold one litre of water using steam in a $500\mathrm{ml}$ container. The steam will be condensed back into water when extracted from the containment chamber. I am not sure of the exact ways... |
In introductory quantum mechanics I have always heard the mantra
The phase of a wave function doesn't have physical meaning. So the states $| \psi \rangle$ and $\lambda|\psi \rangle$ with $|\lambda| = 1$ are physically equivalent and indiscernible.
In fact by this motivation it is said that the state space of a phys... |
This is a question parallel to this question The importance of the phase in quantum mechanics.
In introductionary quantum mechanics I have always heared the mantra
The superposition principle which says that two states of a quantum system can be added to obtain a new state explains the interference we see in the doubl... |
I have an extremely basic doubt about Huygens Principle:
Every point on the wavefront may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wavefront is the tangential surface to all these secondary wavelets.
My doubt is about how many so... |
I am investigating the diffusion of ink in water. A drop of blue ink is dropped to the center of a round plate of radius $R$. Say the drop of ink has an initial radius of $r=r_0$ (the very edge of the drop - there appears to be some "layers" in it), and I want to see how it spreads overtime (see image below).
My first... |
Well, when it comes to electricity generation it is important to design units to be scalable enough.
With wind turbines becoming popular nowadays it is very important.
As you know, currently wind turbines are placed on surface, mostly at hills and small mountains.
But why placing it on surface, where the wind speed is ... |
It's well known in the multi-partite setting that entanglement can't be generated by local operations and classical communication; indeed, this is often taken as one of the defining properties of entanglement measures. I am interested in what bounds have been proven about a single-particle analog.
Let's concentrate on... |
I am trying to plot a graph in Excel describing a free fall of an iron sphere dropped from an altitude of 12 km, while taking into account the different levels of air density affecting the drag.
The function looks like this:
$$v\left(t\right)=\frac{m\cdot g}{b}\cdot \left(1-e^{\frac{-b\cdot t}{m}}\right)$$
where $b$ i... |
I'm implementing a planner for a 6DOF underwater robot and I'm using the dynamics derived in chapter 7.5 of Fossen's Handbook of Marine Craft. I'm using the equations of motion expressed in NED using positions and euler angles in order to use differential flatness control. See equation 7.190.
Part of this is the transf... |
I've read that plane waves are idealizations, but I'm trying to get a mechanical intuition for plane waves. In a classical E&M model, would cycled charging/discharging of a parallel plate capacitor with very large area generate a plane wave, or at least something very close to a plane wave, in regions between the plat... |
So lets get back to the basics in electricity.
As everyone knows, electric current is just a flow of charged particles, so there is nothing special about it.
But what about the type of particles and the differences of produced currents?
To make things simple let's take a look at 2 basic charged particles - protons and ... |
If we switch from one inertial frame to a different inertial frame with a relative velocity of $\mathbf{v}$, we could transform the scalar and vector potentials thusly:
$$\varphi' = \gamma \left( \varphi - \mathbf{A}\cdot \mathbf{v} \right) $$
$$\mathbf{A}' = \mathbf{A} - \frac{\gamma \varphi}{c^2}\mathbf{v} + \left(\g... |
The binding energy of an exciton is usually modeled after the hydrogen atom and varies with charge $q$ as $q^4$. I don't understand why it is $q^4$ and not $q^2$ - If we assume an electron and hole, the interaction energy should vary as $q^2$, right?
|
So, when someone is red-green colorblind, the colors appear the same to them, like this:
Source: https://iristech.co/what-do-colorblind-people-see/
And if you're totally colorblind, then things presumably just appear like they would in a black-and-white movie.
However, this isn't how ultraviolet patterns seem to work.... |
I am confused that whether the positive terminal in physics refers just to a higher potential or a positive charge. This also comes from the fact that anode and cathode are differently charged in Galvanic and Electrolytic cells. But electricity always flows from Anode to Cathode. So is the anode just an indicator of hi... |
At 39:08 of Lecture 28 of 8.01x by Walter Lewin, a water siphon would not work if the distance is over 10 meters due to the barometric pressure. However, this claim is seemingly refuted by Periodic Videos, where at 1:20 he said that the idea that atmospheric pressure pushes the liquid through the siphon is incorrect. A... |
Concerning then the Einstein Field Equations, today we have a plethora of solutions $[1]$, $[2]$, $[3]$. But, when can we call a solution "cosmological"? Because, suppose the Kerr spacetime; region I (the "Minkowski diamond") describes a compactfied universe far from Kerr black hole, i.e., Minkowski spacetime region fr... |
About the familiar formula $Q=I_3 + Y/2$. As an example, the left-handed electron has charge $Q=-1$, weak isospin $I_3 = -1/2$, and weak hypercharge $Y=-1$.
The electron is represented in the Dirac equation by bispinors. For example, Peskin and Schroeder's classic textbook "An Introduction to Quantum Field Theory" uses... |
Taking Schwarzschild spacetime as an example, an observer at infinity can observe events happened in his neighbourhood at infinity and measure the corresponding physical quantities. I want to know whether the observer at infinity can observe events happened at finite $r$.
|
On a river coast, there is a port; when a barge passed the port, a motor boat departed from the port to a village at the distance $S_1 = 15$ km downstream. It reached its destination after $t = 45$ mins, turned around, and started immediately moving back towards the starting point. At the distance $S_2 = 9$ km from th... |
I was going through a paper on a material. In that paper the authors mention "as-grown crystal".
I tried looking for it on Wikipedia and searched it online but none of them tell what it is. So can anyone help?
|
I have a confusion regarding which signal covers more distance - high frequency signal or low frequency signal?
My understanding - high frequency signal has high energy. So, it has the energy to cover more distance.
My confusion - the light from the Sun is usually composed of longer wavelengths and not shorter wavelen... |
Wikipedia and other sources say that the normalized symmetric ket for $N$ particles with quantum numbers $n_1, n_2, ...,n_N$ is
$$|n_1n_2...n_N;S\rangle=\sqrt{\frac{\Pi_km_k!}{N!}}\sum_P|n_{P(1)}\rangle|n_{P(2)}\rangle...|n_{P(N)}\rangle$$
Where $m_k$ is the number of particles in stake $k$. My question is, since for e... |
Rockets launched to reach orbit usually start from a stationary position, engines are started and the rocket slowly gain acceleration upwards, eventually reaching orbit.
What I'm thinking is that the rocket "wastes" a few seconds reaching a speed/acceleration that could be gained by other means. That would save a littl... |
If I have square loop wire with current flowing , can the magnetic field of one segment of a wire mess with other's magnetic field?
If I were to take an observation point perpendicular to a segment wire and at a very far distance, can I just add the magnetic field of 2 (somewhat) perpendicular wire together and omit t... |
I wrote a program that adds force to a car like so:
Engine Force = Power / Velocity
Drag Force = -Velocity²
Net Force = Engine Force - Drag Force = Power / Velocity - Velocity²
I'd like to determine power based on how fast I want a car of a given mass to reach a given speed, for example, 0 to 20 m/s in 10 seconds ... |
Consider a linear spring-mass disordered chain with a large number of masses (say $10^6$ masses). The spring constant $k_i$ of each spring is set to 1. The chain consists of atoms of mass 1 and mass 2 placed randomly such that they have equal concentrations.
The displacements of the particles is given by:
$$ x_{i+1} ... |
I was reading the paper 'A linear response approach to the calculation of the effective interaction parametersin the LDA+U method' by Cococcioni et. al (1)
Quoted verbatim from section 3.A),
In order to fully define how the approach works the first thing to do is to select the degrees of freedom on which 'HubbardU' w... |
Why don't charges pile up at the vicinity of resistor as charge flowing out of resistor is slow at one side of resistor but on the other side charge starts to pile up to enter resistor?
|
Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical temperature (T ~ 2.269). Thats what I got.
Is it correct? The local updated algorithm didn't show the exponential decay i... |
The field of the electric dipole is $\displaystyle\vec{E}=\frac{3(\vec{p}\cdot\hat{r})\hat{r}-\vec{p}}{4\pi\epsilon_{0}r^3}$, show that it can be written as linear combination of $\displaystyle\frac{Y_{2m}(\theta,\phi)}{r^3}$, i.e, $$\vec{E}=\frac{3(\vec{p}\cdot\hat{r})\hat{r}-\vec{p}}{4\pi\epsilon_{0}r^3}=\sum_{m=-2}^... |
The article I was reading states that one factor affecting the occurrence of thin-film interference is the light source. The quality of the light reflecting off a film can impact the amount of iridescence observed.
The “whiter” the light is, meaning the closer it comes to emitting all colours in the visible light spec... |
The energy-momentum relation in special relativity states $m^2 = E^2 - ||p||^2$ (in natural units). So
$$ E = \pm\sqrt{\| p \|^2 + m^2}. $$
If we want to find a theory for a relativistic free particle, one could quantise this expression and use the result as a Hamiltonian. This gives:
$$ H = \sqrt{-\Delta^2 + m^2}. $$... |
As far as I know, Gauss' Law is useful for calculating the electric field where Coulomb's Law doesn't work. For example, it is used for calculating the field produced by a thin sheet of charge and also used for infinitely long thin line of charges.
But in both of these cases, the field can also be obtained using Coulom... |
What is meant by the "general formula for the scattering process"?
In an old exercise my lecturer gave me, I am told to:
Give the Lagrangian for a scalar Yukawa Scattering:
$$\mathcal{L}= \frac{1}{2} \partial_\mu \phi \partial ^\mu \phi - \frac{1}{2} m^2 \phi^2 + \partial_\mu \varphi^* \partial^\mu \varphi - M^2 \varph... |
This is a question from the Berkeley Physics coursebook- Mechanics Vol1
Three forces F1, F2 and F3 act simultaneously on a point particle. The resultant force Fr is simply the resultant force. Show that if Fr = 0, then the vectors representing the three forces form a triangle.
I am really bad at such problems(specifi... |
I was wondering what function describes the form of a whirlpool funnel in a liquid (say, water) rotated by some sort of a paddle sunken at depth in a cylindrical barrel.
To simplify the problem, assume:
water in a cylindrical vessel of large height and a $R$ radius
a cylindrical rod of radius $r$ ($\ll R$), along to... |
How would you draw the diagram for the $D$ meson decay mode:
$$ D^- \rightarrow K^+ + \pi^- + \pi^- $$
|
I have phrased the question as such, to confirm that convolution of the two functions raises the dimensionality of the convolution product. So, if I do convolution of velocity and time, then the resultant should have units of metre x time. Am I correct?
Or an alternative example can be charge Q stored in a capacitor i... |
The Wu experiment is the first experiment to prove parity violation of the weak interaction.
In the experiment, ultra-cold cobalt-60 atoms are aligned in a magnetic field. The cobalt-60 atoms decay to excited nickel-60 atoms by the weak force under the emission of an electron and an electron-antineutrino. The excited n... |
I am currently reading this book by Mireille Levy. It says (on page 40) that the Gaussian beam pattern with half-power beamwidth $\beta$ is gien by:
$$B(\theta)=A\text{exp}\left(-2\text{log}2\frac{\theta^2}{\beta^2}\right)$$
where $A$ is the normalization constant, $\theta$ is the elevation angle and $\beta$ is the hal... |
In Greiner's book of classical electrodynamics there is an example formula of a three-body force between two charges.
For many-body forces the force between two bodies 1 and 2 depends also on the positions of the other bodies $\mathbf{r}_3,\mathbf{r}_4,\dots$. For example, a three-body force would be
$$
\mathbf{F}_... |
I know that the cosmological constant was developed as an addition to the Einstein Field Equation as an anti-gravity force: $$R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}$$
so that he could get a static universe. But later it was discarded. And now it is related to dar... |
Chiral condensation is known to be characterized by the nontrivial expectation value of
$$\langle \chi_{ai}^{\alpha} \xi_{\alpha j}^a\rangle= U_{ij}$$
where $\chi$ is the left handed Weyl fermion and $\xi$ is the right handed Weyl. $\alpha=1,...,N$ is the color index, $a=1,2$ is the spinor index, and $i,j=1,...,N_f$ i... |
While researching cosmic strings, one often encounters terminology ranging from "scaling solutions" to "correlation lengths". As a newcomer, one of the first questions I have had is "how many cosmic strings could there be in the observable universe?". This is clearly a very difficult question, as it is a complex proble... |
Is it possible to make a capacitor between two equipotential surfaces?
I asked my teacher and the explanation given was: There is an electric field between the two equipotential surfaces ( Each equipotential surface at different potential ) , thus energy is stored in the volume and if we discharge the energy, it acts l... |
I understand that in an adiabatic compression, we will do it fast enough to not allow any heat to escape the cylinder. But suppose I can't do it fast enough.
What law - or formula - is used to find the final temperature and pressure of the air immediately after compression ceases? And what quantities, apart from initia... |
I was recently instructed by my instructor that the axis of rotation in the case of a couple always passes through the center of mass and is parallel to torque,Why is this true?
|
My Doubt is regarding the procedure of calculating force on dielectric while it is being inserted between the capacitor plates (with or without battery).
This is the theory behind it.
Consider a capacitor which is charged and disconnected from the battery.
Now the energy stored in the capacitor is calculated by using ... |
I am currently working on a project on fusion reactors and am researching the basics of them. During my research, I encountered "antenna" which produce ion and electron cyclotron frequencies to heat the reactor. Then I encountered cyclotron resonance which brought me to a cyclotron particle accelerator. I then research... |
I'm having some problems trying to work through my university's GR notes, regarding the derivation of the weak field metric from the perturbation of the Minkowski metric. I'll provide the relevant material here.
Now in general we have a perturbed gravitational metric
$$\mathbf{g} = \eta + \mathbf{h}$$
where $\eta$ is t... |
I derive the quadratic form of Dirac equation as follows
$$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$
And I need to find the form of the spin dependent term to get the final expression
$$g \frac{e}{2} \frac{\sigma^{\... |
So I am self-studying mechanics using Marion and, as many books, it uses the notation of the dot over the function to express a time derivative, as in
$$x = x(t)$$
$$\dot{x}= \frac{dx}{dt}(t) $$
The book also uses the bold notation for vectors, like for example the position vector is:
$$\textbf{r} = \textbf{r}(t)$$
Put... |
Consider a horizontal wire loop through which a magnet is dropped. I understand the macroscopic explanation. The moving magnet generates an electric current in the wire loop(counterclockwise when viewed from the top). The wire loop's current then generates a magnetic field in the opposite direction(up). Certainly I hav... |
I'm brushing up my concepts on LASER's and I was just curious about this. Does a three level pumping scheme necessarily imply that exactly three energy states have to be present? Or can more or or less energy states can be present as well? I know that a four level pumping scheme is more efficient but this is just a que... |
A beam of protons with energy $E_p$ is made to collide with a stationary target and a search for the interaction $p + p \rightarrow p + p + \bar{p} + p$ is made.
I have to estimate the minimum energy $E_p$ for this reaction to occur.
I think the minimum energy would correspond to when the produced protons have zero... |
I am reading Lorentz transformation from Robert Resnick book. It is given that
$x'= a_{11}x + a_{12}y + a_{13}z +a_{14}t$
$y'= a_{21}x + a_{22}y + a_{23}z +a_{24}t$
$z'= a_{31}x + a_{32}y + a_{33}z +a_{34}t$
$t'= a_{41}x + a_{42}y + a_{43}z +a_{44}t$
While solving coefficients of $y'$, as the two frames are coincidin... |
I have read this question:
Does an electron's drop from $2s$ to $1s$ produce the exact same type of photon in different atoms and molecules?
where Emilio Pisanty says:
Transitions which change spin direction are electric-dipole-forbidden, and they can only take place from magnetic-dipole onwards, which means that the... |
Can you explain what is the third vector (the one with the tag) in the following equation:
\begin{align}
\vec{L} = \vec{L}_{\text{cm}}+\vec{L}'
\end{align}
|
I’ve been learning the concepts of static equilibrium and the book I’m using is providing examples of objects that are unstable when their center of gravity is outside the area of support. For example, the higher the center of gravity of a car is, the easier it is overturned over a banked road. How to prove that torque... |
The spinor in the Dirac equation should transform via a 4x4 matrix $S$ that depends on the specific Lorentz boost/rotation:
$\psi '(x')=S(\Lambda )\psi(x)\tag1$
Where S satisfies:
$S^{-1}\gamma ^{\mu }S=\gamma ^{\nu }\Lambda _{\nu }^{\mu }\tag2$
(Where the $\gamma^{\mu}$ are the gamma matrices) As to ensure Lorentz in... |
I always thought that a change in electric field induces a magnetic field and vice-versa. Moreover, I imagined that any current distribution will give rise to a magnetic field. But then I wrote this down: Maxwell's equations in absence of magnetic field.
\begin{align}
\nabla \cdot \mathbf{E}(\mathbf{x},t) &= \frac {\rh... |
Consider the hydrogen atom, just taking into account the electrostatic force and not magnetism nor spin.
Is it possible to take the wave functions of the energy eigenstates of that hydrogen atom, appropriately weight each one, and then sum them up in order to get something like a Gaussian wave function of position, or... |
We're given two inertial frames $S$ and $S'$ moving with relative speed $v$. For simplicity, we’ll start by ignoring the directions y and z which are perpendicular to the direction of motion Both reference frames come with cartesian coordinates $(x, t)$ for S and $(x', t')$ for $S'$. Therefore the most general transfor... |
We know there are 5 types of bilinears in 4 dimensions, all of them add up to contribute with 16 independent DoF (degrees of freedom). Namely, these bilinears are known as: scalar (1DoF), pseudoscalar(1DoF), vector(4DoF), pseudovector(4DoF) and tensor (6DoF).
How do we know there are only 16 independent DoF in 4 dimen... |
In Quantum Physics it is postulated that, any general state $\psi$ can be represented as superposition of eigenstates with constant coefficients corresponding to any observable.
Say, I have all the eigenstates of energy, then I can represent wavefunction $\psi (x)$ as superposition of eigenstates of energy. But from th... |
Suppose I have a sphere with radius $R$ and charge $Q$ and another hollow sphere with inner radius $2R$ and outer radius $3R$ with charge $2Q$, both of them are conductive.
I want to calculate the charge density on the surfaceses of the 2 spheres. for the inner one its easy because the desity is uniform its just $$\sig... |
On Gravitation Page 286 Exercise 11.7, it mentioned a very interesting operator called "Jacobi curvature operator"
$${\cal J}(u,v) n\equiv \frac{1}{2} [{\cal R}(n,u)v +{\cal R}(n,v)u ]$$
where it "contained the same information continent as Riemann", and
in component form (Eq. 11.36)
$$J^\mu_{\nu \alpha \beta} =\fra... |
Similar questions have been asked here, but there's one part of this that I don't understand; in a resistor connected in a circuit, as the energy of the electrons decreases when they pass through the resistor, shouldn't the difference in potential across a resistor increase?
And, therefore, shouldn't the terminal pote... |
the magnetic field moves in a loop right? How long does it take to go from one pole to another?
|
My teacher was solving the Brachistochrone problem in class. She parametrized the required path with $x(y)$, then said $T=\int_0^Tdt=\int_{y_1}^{y_2}\frac{dt}{dy}dy=\int_{y_1}^{y_2}\frac{dy}{dy/dt}$. Why is this conversion from $dt/dy$ to $dy/dt$ allowed? There is a similar question on math stack https://math.stackexch... |
I am very tired and in this moment I have not think very well. Using the vectorial expressions of the magnetic and electric field if an electromagnetic wave propagates in a certain direction the electric field and magnetic field are always perpendicular to each other. They arise from Maxwell's equations in the absence ... |
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