# Search results

1. ### Show that the radiation field is transverse

Homework Statement Show that the radiation field is transverse, ##\vec{\nabla}\cdot\vec{A}=0## and obeys the wave equation ##\nabla^2\vec{A}-\frac{1}{c^2}\partial_t^2\vec{A}=0##. You should start from the expansion of the quantum Electromagnetic field. Homework Equations ##H=\frac{1}{2}\int...
2. ### Dirac hydrogen atom vs spin symmetry

Homework Statement Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...
3. ### Energy levels of a system with just two electrons?

Homework Statement If a system comprised only of two electrons was physically possible (such as positronium but with two electrons), what would its energy levels be and how would they relate to the energy levels of Helium? Homework Equations ##E_{Helium} = E_{n1}+E_{n2}=-\frac{\mu Z^2...
4. ### I How can I access event data for LHCb calorimeters?

I want to do a project using machine learning on the calorimeter event data of the LHCb. How can I access this data? Is it very difficult to navigate your way through the source code on your own?
5. ### Using Noether's Theorem find a continuity equation for KG

Homework Statement Consider the Klein-Gordon equation ##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0##. Using Noether's theorem, find a continuity equation of the form ##\partial_\mu j^{\mu}=0##. Homework Equations ##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0## The Attempt at a Solution...
6. ### Potential energy of moving charge in field

Homework Statement 1. Homework Statement [/B] Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}## Homework Equations...
7. ### Prove ∇ × J = 0 means B=0

Homework Statement Prove that a current density J(r, t) such that ∇ × J = 0 implies the magnetic field B = 0. Homework Equations Maxwell's equations, vector calculus The Attempt at a Solution I've played around with Maxwell's equations and with the properties of vector calculus but I...
8. ### Velocity of propagation of an EM field in vacuum

Homework Statement In a region of empty space, the magnetic field is described by ##\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}##. Find the speed of propagation ##\vec{v}## of this field. Homework Equations ##\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}## , ##k=\frac{\omega }{...
9. ### Relationship between density and probability in diffusion

Homework Statement Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##? Homework Equations...
10. ### What is the equilibrium angle - dipoles?

Homework Statement Two coplanar dipoles are oriented as shown below. If θ is fixed, what is the equilibrium angle θ' ? Homework Equations The torque exerted by dipole P on dipole P' is given by $$\vec{N'}=\vec{P'}\times\vec{E}$$ where vector E is the electric field. The Attempt at a...
11. ### Estimate the latent heat of water

Homework Statement Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens? Homework Equations $$ΔQ=TΔS=L$$ $$S=nR[\ln(\frac{(V−nb)T^{3/2}}{nΦ})+\frac{5}{2}]$$ The Attempt at a Solution I predict the latent heat of vaporization of...
12. ### Estimate the latent heat of water with Van der Waals

Homework Statement Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens? Homework Equations $$\Delta Q = T\Delta S=L$$ $$S=nR\left[ \ln\left(\frac{(V-nb)T^{3/2}}{n\Phi}\right)+\frac{5}{2} \right]$$ The Attempt at a Solution I...
13. ### Chemical potential of water using the Van der Waals model

Homework Statement Obtain the chemical potential of water as a function of temperature and volume using the Van der Waals model. Homework Equations μ=∂U∂N The Attempt at a Solution I don't really understand how to do this at all. Any help would be greatly appreciated.
14. ### Prove the Langrangian is not unique

Question: If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations show by direct substitution that http://qlx.is.quoracdn.net/main-74d090d14ee4fea0.png [Broken] also satisfies Lagrange's equations where F is any arbitrary but differentiable function of its...
15. ### Callen Thermodynamics 2.8-2 matter flow equilibrium

Homework Statement A two component gaseous system has a fundamental equation of the form $$S=AU^{1/3} V^{1/3} N^{1/3} + \frac{BN_1N_2}{N}$$ where $$N=N_1+N_2$$ and A and B are positive constants. A closed cylinder of total volume 2V_0 is separated into two equal subvolumes by a rigid diathermal...