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So, I know that $\oint \frac{\delta Q}{T}\le0$ , that's the inequality and it's equal to 0 for reversible and less than 0 for irreversible. But at the same time I know $\Delta S=\oint \frac{\delta Q_{rev}}{T_{surr}}$ and $\frac{\delta Q_{rev}}{T}\ge \frac{\delta Q}{T}$ coming from the Planck-Kelvin statement of the second law of thermodynamics. But doesn't this just mean that $\Delta S \ge \oint …

I was recently intereseted on Continuum mechanics and it's relationship with integration, manifolds and General Relativity. I'm interested in the connection of Continuum mechanics with General Relativity, specially with the relationship of the stress tensor $\sigma_{ij}$ with the energy-momentum-stress tensor $T_{\mu \nu}$ . I want to deeply understand the stress tensor, in order to understand it…

Let's say I want to calculate the wavelength of the photon emitted when an electron of an arbitrary element (let's say Carbon) drops from $n=4$ to $n=3$ . Correct me if I'm wrong, but I think I would have to find the change in the electron's energy value $\Delta E = E_i - E_f$ , set that equal to $hc/\lambda$ and solve for the wavelength ( $\lambda$ ). How could I find $E_f$ and $E_i$ ? My textbo…

Chemist here - thus a probably stupid physics related question. I will spare you the details and the background and try to break it down: (Assumably) I am looking at a system of lamellar micelles that have a somewhat defined mean interlamellar distance. These can reflect light and at a certain angle the bragg equation can be satisfied so that constructive interference can occurr. So let's say we …

Chemist here - thus a probably stupid physics related question. I will spare you the details and the background and try to break it down: (Assumably) I am looking at a system of lamellar micelles that have a somewhat defined mean interlamellar distance. These can reflect light and at a certain angle the bragg equation can be satisfied so that constructive interference can occurr. So let's say we …

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 series. I can get $E = Vd$ and $V = E_1d_1 + E_2d_2$ but I don't know how to get th…

Is energy really the ability to do work? For 219;years we have been using young's definition. Because in the 1807 all they had was steam engines and cannons. Everything that 'had energy ' was literally pushing pistons or firing balls. So 'work' made sense back then!

Would a rotating sphere of magnetic monopole charge have electric moment? In a duality transformation $E\rightarrow B\cdot c$ etc. how is the magnetic moment translated $m = I\cdot S $ ? $M_{el} = \frac{d}{dt}(-\frac{Q_{mag}}{c})\cdot S$ ? A more general question would a sphere charged with monopoles have other moments that the monopole in the multipole expansion? Like electron is predicted to ha…

The below image is from the book Concepts of physics by H.C. Verma. The last line says that if pulley $B$ is also light then $T_1=T_2$ I don't understand how this happens.

I am trying to understand what's going on with this problem: I summed the forces in the $x$ -axis, which is horizontal, and I thought the moment would create a force opposing the friction force. However, the given solution only included the friction force: $$F_\text{friction} = ma.$$ My equation was: $$F_\text{friction} - M/r = ma.$$ Why is the force caused by the moment excluded? Is it because t…

According to standard electromagnetic theory, if the charge A is stationary and the charge B is moving along arbitrary trajectory then the electromagnetic force on charge A is: $$\vec{F}_A = q_A \left(-\nabla\phi - \frac{\partial}{\partial t}\vec{A}\right)$$ where $\phi$ and $\vec{A}$ are velocity dependent scalar and vector potentials (Lienard-Wiechert potentials), i.e. $$\phi = \frac{1}{4\pi\ep…

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \langle |\hat {T}\left( \hat {O}_{l}(x_{1})\hat {A}_{2}(x_{2})...\hat A_{n}(x_{n})\right) |\rangle , \quad (1) $$ where $\hat {O}_{l}(x)$ transforms under the irreducible representation of the Lorentz gr…

Why is it that, in general, the particles produced/emitted during a given particle collision tend to be produced/emitted at angles relative to the beam axis? I can kind of see why this is true for collisions between composite particles, since then, using a classical analogy, as they collide the constituent particles will not necessarily experience a "head-on" collision - if they are not inline wi…

Suppose a Hilbert space has a direct-sum decomposition $$ \mathcal H=\bigoplus_{n\ge 0}\mathcal H_n, $$ where the sectors are eigenspaces of a self-adjoint operator $\hat S_c$ , $$ \hat S_c|\psi_n\rangle=s_n|\psi_n\rangle. $$ Let $\hat J$ be a self-adjoint generator of unitary evolution, $$ U(\tau)=e^{-i\hat J\tau}, $$ and suppose $$ [\hat J,\hat S_c]=0. $$ A separate clock/phase operator $\hat S…

Newton, in his "Principia", already noticed that rotational movement does not depend on an external reference frame, because, even without any external reference, an observer in a rotating bucket can determine his state of movement through the appearing of centrifugal and Coriolis forces. Rotational movement is absolute. Quantum mechanics, too, attributes rotation an absolute value, because the s…

I'm trying to write a Python code to implement Hartle-Thorne approximation formalism for rotating neutron stars. In this formalism, I am required to solve the following second order differential equation: $$ \frac{1}{r^4}\frac{d}{dr}(r^4 \frac{d \bar{\omega(r)}}{dr}) + \frac{4}{r}\frac{dj(r)}{dr}\bar{\omega(r)} = 0$$ with the boundary conditions $\bar{\omega}(r=0) = \bar{\omega_c}$ and $\frac{d\b…

According to the Lensmaker's formula , $$\frac{1}{f} = (μ-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$ Apparently, focal length $f$ is inversely proportional to the refractive index of the medium $μ$ . Since, Optical Power $P = \frac{1}{f}$ . This should imply that optical power is directly proportional to the refractive index. However, today I got told by my teacher that these two are independ…

An exercise in Schutz's general relativity book states: "A body is said to be uniformly accelerated if its acceleration four vector $\vec{a}$ has constant spatial direction and magnitude, say $\vec{a}\cdot \vec{a} = \alpha^2$ " . Unfortunately, I don't understand what's meant by "constant spatial direction". I can find an explicit solution if, in a given referential frame, the speed is given by: …

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that far above the plate, the field should approach the dipolar field which scales as $1/r^3$. However my numerical calculations are yielding $1/r^4$. I am using Jackson's book (3rd ed.) as a guide. I as…

The Hamiltonian of a free particle in a rotating frame is given by $$ H = H_0 - \omega \cdot J, $$ where $H_0$ is the Hamiltonian in the non-rotating frame, $\omega$ is the angular velocity of the frame and $J$ is the angular momentum of the particle. This relation is too beautiful to be a coincidence. Does it hold for arbitrary systems with rotational invariance? Is a more general statement poss…