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How to derive $\partial^{\nu}F^{\mu\alpha} + \partial^{\alpha}F^{\nu\mu} + \partial^{\mu}F^{\alpha\nu}=0$ for the Electromagnetic field tensor?

Write down $\partial_\mu G^{\mu\nu} = \frac{1}{2}{\epsilon^{\mu \nu \alpha \beta}\partial_\mu F_{\alpha\beta}}$. Now, fix the free index $\nu$ (to be either of 0, 1, 2, 3), and write down all non-zero ...
Archisman Panigrahi's user avatar
0 votes

Trouble in complex integral while calculating 2-point function in AdS-CFT correspondence

By integrating $$ \int_C e^{iz} z^{\alpha-1}dz $$ about the boundary of the first quadrant and taking the imaginary part, one can show that $$ \int_0^\infty x^{\alpha-1} \sin x dx=\Gamma(\alpha)\sin (\...
mike stone's user avatar
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0 votes

Components of velocity in projectile motion

The ball's (resultant) velocity $\vec v$ is the vector sum of its horizontal component $\vec v_x$ and vertical component $\vec v_y$, i.e., $\vec v=\vec v_x+\vec v_y=v_x\hat i+v_y\hat j$. This is ...
Pustam Raut's user avatar
0 votes

Static friction with ground when two blocks have different coefficients

If the first block can withstand the pushing force $F$ (if the friction $f_1$ can be large enough to achieve $f_1=F$), then there is no need for the second mass to exert any force, and so $f_2$ would ...
Steeven's user avatar
  • 51.1k
0 votes

Components of velocity in projectile motion

The horizontal velocity does not change during the fall. So the total velocity can be inferred from the angle given.
Confuse-ray30's user avatar
1 vote
Accepted

What exactly is the normal force?

If Mr. B's mass is half of Mr. A's mass, then the normal force must be adjusted to half, and Mr. B will also perform the same circular motion as Mr. A. The gravitational force and the centripetal ...
KDP's user avatar
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1 vote
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Where am I going wrong when obtaining the Hamiltonian density for the electromagnetic field?

Hints: Instead of OP's eq. (5) the prescription of the Legendre transformation is to eliminate the velocity variable $$ \dot{A}_i~\equiv~\partial_0A_i~=~F_{0i} +\partial_i A_0 \tag{5'}$$ by ...
Qmechanic's user avatar
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0 votes

Phase shift in a film

The reason is that you have to consider the wavelength of the light inside the film which is different from that in vacuum/air. In particular, when light travels through a media with refractive index ...
Tommaso Gallo's user avatar
0 votes

Kohn-Sham equations from variational principle

The Kohn-Sham equations arise from variation in terms of orbitals, not the total density. See for example Fundamentals of DFT by Eschrig, 2nd ed., Sec. 4.2.
Mage's user avatar
  • 3
0 votes

Spherical harmonics integral

This is the formula relating $Sin(\theta)e^{-i\phi}Y_{lm}(\theta,\phi)$ from "Mathematical Methods for Physicists" by George B. Arfken and Hans J. Weber. Using this formula and then the ...
Pawan Kumar Gupta's user avatar
0 votes

How to minimize the term of frictional force proportional to velocity square?

If those data you collected (mentioned in the question) is the amplitude of those damped oscillations vs. time, then you can determine $C_1$ and $C_2$ separately for both types of disk. We would ...
Jos Bergervoet's user avatar
0 votes

C-15 spin and parity at ground state

Because there is still room in 1p(1/2). The protons only fill up to 1p(3/2).
Ytterby's user avatar
0 votes

Calculating Eigenkets of Perturbed Matrix for Second-Order Correction

While the equation for the second-order correction \begin{equation} E_n^{(2)} = \langle n^0 | H^1 | n^1 \rangle \end{equation} Is correct, I found that it is more useful to put that equation in its ...
PineappleThursday's user avatar
2 votes

Transformation of wavefunction

It is obvious that $\psi_B(x_B,t)=\psi(x_B-vt,t)$ because $x$ at $t$ and $x_B-vt$ at $t$ denotes the same point. This is where your mistake starts. Wavefunction is not an observable, so you can't ...
Ruslan's user avatar
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2 votes

How does $g$-force work?

"G-Force" is a colloquial term. However, it is indeed a very common one. G-forces show up most commonly in systems where one is constrained to accelerate at a certain rate (although you ...
Cort Ammon's user avatar
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-1 votes

Hi, how should I solve this problem? Thanks

Remember a force causes acceleration, thus there will be a non-constant velocity in any direction where there is an acting force. If the velocity in a direction is constant, then there is no force in ...
Albertus Magnus's user avatar
0 votes

Why don't we take kinetic energy into account when finding the change in potential energy?

Good question. The problem is an incompletely described situation. Such questions are common, and it's up to the reader to make reasonable assumptions about the missing information. In the case you ...
garyp's user avatar
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0 votes
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Can I solve the drag equation without any experimental data? (I have a 3d model of a rocket and want to see how fast it can go using math)

The reference area moving upward is the top down view. You probaly don't intend for the rocket to move sideways. But you'll have to guess the drag coefficient, maybe 0.5. If you have a supercomputer, ...
John Doty's user avatar
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0 votes

How to find the other positive velocity?

You did the problem correctly. Since the shell is on the way down when it impacts the cliff edge, the shell lands at a distance zero passed the edge. There is no other velocity that can hit the cliff ...
Mark H's user avatar
  • 24.1k
1 vote

Variation of the Einstein-Hilbert action to derive the metricity condition

To see that this implies the covariant conservation of the metric, we simply look at some of the traces and contractions of the equations presented here. For instance, tracing over $\mu$ and $\rho$ ...
Eletie's user avatar
  • 3,263
1 vote

Confusion in conservation of momentum

Remember that the vector sum of bodies' momenta is conserved provided that no forces act on the bodies except forces between the bodies themselves. If the masses are the bodies in your system (and the ...
Philip Wood's user avatar
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0 votes

Photon Escape Angle From Black Hole

$$\newcommand{\l}[0]{\left(1-\frac{2\mu}{r}\right)} \\ \newcommand{\lz}[0]{\left(1-\frac{2\mu}{r_0}\right)}$$ This was in the 2022 3rd year Cambridge exam, with no official solution so I came here. In ...
Harvey Williams's user avatar
2 votes
Accepted

Multiple cavities in a conductor and a charge outside

You are right that $\vec E_4=-\vec E_3$ but neither of them is zero. If the book says $\vec E_4=\vec E_3=0$, then the book is wrong (unless it defines $\vec E_3$ and $\vec E_4$ differently than you do ...
Jos Bergervoet's user avatar
1 vote
Accepted

Why centripetal acceleration does not causes the rotating particle to reduce the radius of its circular path?

Centripetal velocity constantly increases in terms of magnitude Just think about it, what you are saying would work in the case when the body is in rest ( but that's not the case , it is rotating ). ...
CP of Physics 's user avatar
0 votes

Unsubstantiated assumption in a problem about two particles rotating around each other

You can use kinematics of circular motion to solve this. As the bodies perform uniform circular motion about each other, it means that with respect to one of the bodies, the velocity of other body is ...
EagerToLearn's user avatar
1 vote

How to calculate the inner product $ \langle T|x \rangle = \langle\frac{p^2}{2\mu} |x\rangle$?

Indeed, in your odd notation, for $\hat T =\hat p^2/2\mu$, a good (overgenerous!) basis for the eigenstates of $\hat T$ would be $|p\rangle$. Both signs of p will yield the same doubly degenerate T ...
Cosmas Zachos's user avatar
2 votes

Heat exchange speed of two liquids separately vs their mixture

So I ran my own experiment, and tried to make it as rigorous as my kitchen allows it. I don't have any way to measure temperatures exactly, but I have kitchen scales The setup: 3 identical cups, of ...
Alexey S. Larionov's user avatar
1 vote

Weinberg Chapter 19.5, pion scattering amplitude derivations

I also have been struggling to read Weinberg QFT and could not find my way out from Chapter 19 deriving Eqs. 19.5.25 and 19.5.29. Fortunately, somehow I find my exit path and would like to share it ...
HitoshiMomma's user avatar
1 vote
Accepted

Heat exchange speed of two liquids separately vs their mixture

It looks like the 2 procedures don't provide the same result. In what follows, it's assumed that: initial milk temperature is the same as the environment temperature, $T_{env}$ no heat or work ...
basics's user avatar
  • 9,010
0 votes

Pressure of the air in a hot air ballon?

If there had been a pressure difference between the air inside and air outside there would be air flow till equilibrium is achieved again. Had the balloon been closed from the bottom restricting ...
Sammybro11's user avatar
1 vote

Determining Critical Temperature of Oxygen from Six $p$-$V$ Diagrams

Without trying to reproduce your plots, it seems like you are plotting in a wrong way. Some hints: The part below $V=b$ with negative pressure is not physical. Don’t plot it. Use logarithmic axes. ...
Wrzlprmft's user avatar
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0 votes

Deriving expression for gravitational potential energy around a mass, $M$, using vectors

We have the dot product: $$\hat r\cdot d\vec r=|\hat r|\cdot|d\vec r|=dr$$ Because the unit vector $\hat r$ and differential displacement vector $d\vec r$ are in the same direction. Note that the ...
Pustam Raut's user avatar
-1 votes

What happens when literally 1 or 2 photons passes through a single slit or double slits?

(a) The total energy that is being emitted by the source in a single burst is spread out uniformly over the wavefront having a total cross-sectional area of $10$ mm$^2$ (as shown in the above figure). ...
Souparna Nath's user avatar
2 votes
Accepted

Speed of satellite in elliptical orbit

Velocity in elliptical orbit is not equal to circular (or called orbital) velocity. Given $r1$ and $r_2$ as you defined, $a=(r_1+r_2)/2$, the semimajor axis of the ellipse. Then the vis viva equation ...
W H G's user avatar
  • 401
0 votes

How do Relativity explains electromagnetic induction in the case of changing $\bf{B}$ with both loop and magnet at rest?

If you know how a particle that is moving due to relativistic effects, it will create what we call magnetic field around itself that will rotate. With this, you can relate relativity with the ...
user402553's user avatar
1 vote

Why is time not a significant variable in the amount of potential energy an object has?

the object has more potential energy because there is a longer time for gravity to act on it No. If an object of mass $m$ is at a height $h$ and going up, it has the same potential energy of another ...
Claudio Saspinski's user avatar
4 votes
Accepted

The Klein-Gordon Propagator According to Peskin and Schroeder (Derivation of *Retarded* Green's Function)

There are several ways ways to do the calculation, with the Residue Theorem. Either you foresee that this is an instance of this theorem, or you know the solution and do reverse reasoning to find back ...
Jeanbaptiste Roux's user avatar
0 votes

Potential attained by a sphere under illumination

In the conventional photoelectric effect, the stopping potential is the potential difference between the metal surface and the collecting electrode such that no current can reach the collecting ...
Michael Seifert's user avatar
0 votes
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Potential attained by a sphere under illumination

As the sphere loses electrons, electrons begin to feel an electrostatic attraction to the sphere. When the electric potential attained by the sphere is equal to the maximum kinetic energy of the ...
user1070280's user avatar
0 votes

Question regarding projecticle in freefall disregarding air resistance

This equation: $y(t)= y_0 + v_0 t -1/2gt^2$ describes the complete vertical motion from the moment the stone is thrown of the tower $t=0$ to the moment the stone hits the ground. So solving: $y_0 + ...
Hubert van Luytelaar's user avatar
0 votes
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Question regarding projecticle in freefall disregarding air resistance

If you want to split the trajectory into two parts like this, then the second part of the trajectory will start with the projectile traveling downwards, not upwards. You can show that for this ...
Michael Seifert's user avatar
0 votes

Why is velocity proportional to radius in a spherical explosion?

The assumption is that of uniform expansion at the instant of explosion.
my2cts's user avatar
  • 24.5k
0 votes

Rescaling time in differential equations

It is the non-dimensionalization of the last two differential equations. Assuming $g$ as the acceleration due to gravity ($\text{m}/\text{s}^2$) and $l$ as the length (m), $\sqrt{l/g}$ has the ...
Pustam Raut's user avatar
3 votes
Accepted

Rescaling time in differential equations

It's an usual procedure in deriving non-dimensional equations, from the dimensional ones: angles have no physical dimensions, they wanted a "scaled" (non-dimensional) time as well. You just ...
basics's user avatar
  • 9,010
1 vote

Circular motion school problem

Angular velocity is the rate of change of angular displacement: $\omega = \Delta \theta / \Delta t$ The ride does not rotate any faster or slower despite the person throwing the rock. The speed of the ...
MrDoppler's user avatar
0 votes

Taking functional derivatives of generating functional

Be careful. Your first line is correct, but the statement in the second line is not. You can only use it inside the integration to get rid of the delta function. As I will show you how to compute the ...
Everlin Martins's user avatar
1 vote

Taking functional derivatives of generating functional

My main confusion is about how to take derivatives of function like $J(y_1)$ wrt to $J(x)$. For example what is the value of $$\frac{\delta J(y_1)}{\delta J(x)}$$. Is that equal some kind of delta ...
hft's user avatar
  • 20.7k
2 votes

Kinetic energy of an ellipsoid

$\def \b {\mathbf}$ Landau used this transformation matrix between the local ellipsoid system and inertial system $$\b R= \b R_x(\theta)\,\b R_z(\phi)= \left[ \begin {array}{ccc} 1&0&0\\ 0&...
Eli's user avatar
  • 12.3k
2 votes

Kinetic energy of an ellipsoid

Let $\hat{\mathbf{x}}_1, \hat{\mathbf{x}}_2, \hat{\mathbf{x}}_3$ denote the body-fixed principal axes. There are two angular velocities: $\boldsymbol{\omega}_{AB}$ and $\boldsymbol{\omega}_{CD}$. It ...
Vincent Thacker's user avatar
2 votes
Accepted

Analyzing limiting case in a statics problem

Take the sum of the torques abbaut point A , you obtain $$ M\,g\,\cos(\theta)\frac L2-F\,x=0$$ thus $$ F=\frac {M\,g\,\cos(\theta)\frac L2}{x}\tag 1$$ with $~x=\frac {l}{\tan(\theta)}~$ you obtain $$F=...
Eli's user avatar
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