Density Definition and 1000 Threads

I don't even know where to start... could you please show me step by step

I do not have the solutions to this problem so I'm wondering if my attempt is correct. My attempt at solution: We have two surfaces which we can calculate the area of. I think we can use gauss law to find the electric field and then integrate the E-field to find the electric potential. So for...

I'm trying to understand the detailed concept of why the density of states formula is accurate enough to calculate the number of quantum states of an energy level, including degeneracy, within a small energy interval of ##dE##. The discrete energie levels are calculated by $$E = \frac{h^2 \cdot...

I am trying to calculate the interaction energy of two interpenetrating spheres of uniform charge density. Here is my work: First I want to calculate the electric potential of one sphere as following; $$\Phi(\mathbf{r})=\frac{1}{4 \pi \epsilon_{0}} \int...

I am confused whether for electron I have to use rest mass energy (moc2 + 0.8 MeV) or just 0.8 Mev for calculating E. Also how do I find minimum density of a neutron star using above data ? Please help !

a) Here I used the definition of current (reference: Tong notes, page 14) $$j^{\mu}_{\nu} = \frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi_a )} X_a (\phi) - F^{\mu} (\phi), \ \ \ \ \ \ \ \ \delta \mathcal{L} = \partial_{\mu} F^{\mu}; \ X_a (\phi) = \delta \phi_a$$ In our problem we...

I'm given the following density of states $$ \Omega(E) = \delta(E) + N\delta(E-\Delta) + \theta(E-\Delta)\left(\frac{1}{\Delta}\right)\left(\frac{E}{N\Delta}\right)^N $$ where $ \Delta $ is a positive constant. From here I have to "calculate the canonical partition function as a function of $$...

The body is a small ball. The experiment consists in dropping this ball, while varying the diameter each 3 trials, in a viscous liquid and measuring its falling time: ##D_i\sim t_1,\,t_2,\,t_3##. The equation we are using is: $$\frac{\Delta x}{\Delta...

Most undergrad textbook simply say that it is intuitive that boundary conditions should not play a role if the box is very large. Other textbooks suggest that this should be taken for granted since the number of particles at the surface are orders of magnitude smaller that the number of bulk...

a) Alright here we have to use Euler-Lagrange equation $$\partial_{\alpha} \Big( \frac{\partial \mathcal{L}}{\partial(\partial_{\mu} A_{\nu})} \Big) - \frac{\partial \mathcal{L}}{\partial A_{\nu}} = 0$$ Let's focus on the term ##\frac{\partial \mathcal{L}}{\partial (\partial_{\alpha}...

Here is the question that is is given to me Part a: Part b: I have given this a go and was wondering if my answer seems reasonable. I had worked out that the mass per unit length (mu) is also the density * cross sectional area of wire Thanks!

This is probably a stupid question but i don't want to make a stupid mistake here, so i thought better ask: I'm starting with the simple free Schrödinger Equation ##V(x)=0## (can be 1 dim) and an initial condition where the wave function is somehow constrained to be entirely localized around a...

Yes, pressure is same along the line for both the tubes since the liquids are in equlibrium. (I ignore the slightly longer air column in the left compared to the right). Is my answer correct?

How many nanoseconds after the Big Bang was its energy density that achievable in modern particle accelerators?

I feel like I'm going around in circles trying to do something with the expression ## tr( \rho *log(\rho)) ##. I thought about a Taylor expansion, but I don't think there's a useful one here because of the logarithm. We learned the Jacobi's formula in class, but I don't think I want a derivative...

I am trying to determine the flow of mechanical power through a structure like a drive shaft or even a simple lever. The components of the Cauchy stress tensor, ##\sigma_{ij}##, have units of force/area, so if I multiply by the velocity, then ##\sigma_{ij} v_j## would have units of power/area...

My answer : Both pressures are equal, i.e. ##\boxed{P_A = P_B}##. Reason : (1) The block of wood displaces an amount (mass) of liquid equal to its weight (archimedes' principle for floating bodies, or law of floatation). Hence we can imagine removing the block in the second case and filling it...

I'm trying to understand the relationship between the "number" of field lines passing through a region and the magnetic force in this region.I understand that the drawings are of course conceptual: we cannot draw "all" the field lines (although can be visualized with iron fillings).Also the...

http://astronomy.swin.edu.au/cosmos/B/Big+Bang D (density) = m/V At t = 10^-47, D = 10^93 kg/cm ^3, r = 10^-57 meters, V = 4pi(r^3)/3 which is about (4/3)pi(10^-171)(meters^3) t = 10^-47 precedes the inflationary epoch at t = 10^-35, this is important since this implies all matter at the big...

This is for an experiment to deflect a 28 SWG wire between two magnets, 3cm apart, by passing a current through it (example attached). The force on the wire is obviously F = BIL, but the wire will be passing at 1.5cm from each magnet so there will be some significant fall off of B and I can't...

What is the mathematics involved with calculating the energy lost from sound as it passes through different mediums? If I started off with a 70dB(A) sound wave, and after 0.5m it passed through 10mm of mild steel - what would be the sound level (in dB) 1m away from the steel plate? To clarify...

We understand that the crucial thing about the problem is that the volume of water present in the three containers are not the same. Also, we note that in each case the weight of the container is the total weight of its contents. (A student might be confused as to why should be so - after all...

In Special Relativity I'm given the energy-momentum tensor for a perfect fluid:$$ T^{\mu\nu}=\left(\rho+p\right)U^\mu U^\nu+p\eta^{\mu\nu} $$where ##\rho## is the energy density, ##p## is the pressure, ##U^\mu=\partial x^\mu/\partial\tau## is the four-velocity of the fluid. In the...

So I have to find an expression for ##\vec{A}(\omega)##, $$\vec{A}(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \vec{A}(t)e^{i\omega t} dt.$$ This point is where my confusion comes up. In the answer sheet they integrate over the retarded time ##t_r##, so the integral is...

I am trying to find some nice explanatory books about cosmological perturbation theory. I looked at Longair, Peacock, and Liddle. Even their level is nice, it seems to me that they are explaining things in a bit complicated way. Is there a nice textbook, articles, lecture notes that you guys...

I am trying to choose Elevator wire, chart shows max load reading in KG/m. Does it mean if length increases weight will increases as well ? Example; If max load of wire is 0.492kg/m. And i am using 2 meter does it mean capacity of wire would be 0.984 kg/m.

https://www.wired.com/story/a-bizarre-form-of-water-may-exist-all-over-the-universe/ Black iceI knew the Black Ice Theories since around 1990 https://www.nature.com/articles/s41586-019-1114-6 -- Demontis, P., LeSar, R. & Klein, M. L. New high-pressure phases of ice. Phys. Rev. Lett. 60...

Based on the conditions, I found that $$V(x)=\frac{a^2}{\pi^2} ρ_0sin(πx/a)$$ would be a solution to Laplace's equation for $$|x|\leq a$$ and $$V(x)=cx+d$$, where c and d are constants. From the boundary conditions, $$\frac{dV(a)}{dx}=\frac{a}{\pi} ρ_0cos(πa/a)=ac$$, $$c=\frac{a\rho}{\pi}$$ and...

How would I tackle a problem like this? I made a start by writing down the ideal gas equation and then done some manipulation on both sides to get the density expression of the ideal gas. I'm not sure if this is what the question wants as I'm dealing with 2 different types of gases in the same...

q = 1.602e-19C mass_electron = 1.098e27 c = 3e8 Omega(Mag_flux_den) = 5GHz Lorentz factor = 100 synchrotron radiation at frequency v = 5GHz Mag_flux_den = (Omega(Mag_flux_den) * c * Mass_electron * Lorentz factor) / mass_electron Mag_flux_den = (5000 x 3e8 x 1.098e27 x 100 ) / 1.602e-19 =...

Inner conductor radius = 1cm outer conductor radius = 10cm region between conductors has conductivity = 0 & 𝜇r = 100 𝜇r = 1 for inner and outer conductor Io = 1A(-az) 𝑱(𝑟) = (10^4)(𝑒^-(r/a)^2)(az) Problem has cylindrical symmetry, use cylindrical coordinate system. Find the total current...

I'm confused on how units work with regards to the Fourier Transform (CTFT). I was reading the Wikipedia article on spectral density. In an example, they use Parseval's equation, along with the units calculated on the time side, to determine the units on the frequency domain side. The units of...

If we start with the Lagrangian \begin{equation} \begin{split} \mathcal{L} = & \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}\mu^2 \phi^2 - \frac{1}{4}\lambda^2 \phi^4\\ \end{split} \end{equation} and give the scalar field a VEV so that we can define the field ##\eta##, where $$\eta = \phi...

Show that ##v_{av}=\frac{\hbar k_2 + \hbar k_1}{2m}## is equal to ##v_{av}=\frac{\omega_2 - \omega_1}{k_2-k_1}##. Which of the identities listed above (if any) would make the sign change between ##k_2## and ##k_1##? One can attain a "wave packet" by superposing two or more sinusoidal waves...

Does anyone have an equation for the resultant density of the composite materials? Having a look around the internet and I can't find anything, there was this one website that gave me a step-by-step but the answers did not match (sciencing.com)

How do I calculate the density of a supercritical fluid? If I have 100 Litres of Xenon at 23°C and 150bar, What will the Xenon in the tank weigh? The phase diagram is here https://encyclopedia.airliquide.com/xenon

I can get the P2 from P1V1=P2V2 --> P2 = 10Bar, but then how do i get the density? p=p/R*T ? where p=10Bar R=287J K-1kg and T 288K, density would be 12,1kg/m3? Is that right?

In most standard exposition of (the mean-field theory of) charge density wave (CDW), phase and amplitude fluctuations are introduced as the collective excitations. Kohn anomaly in the acoustic phonon dispersion is also mentioned as temperature goes from the above till the CDW transition...

See image

I have unfortunately no attempt for 31.i. I don't know how to start the problem. 31.ii is attached. Can someone give me a tip on how to start 31.i? I also have troubles solving 29.iii. I have attached that as well.

If I am given that the density matrix of an incoming beam of spin 1 particles of the form $$p_o=(1/3)[|1><1|+|0><0|+|-1><-1|]$$, aand I needed to find the fraction of particles that would be found with a spin x component of zero, how would I go about solving this problem? My hunch is that I...

We never learned how to use these formulas, so I'm pretty much grasping for straws. I got 2.04 kg/m^3. Can anyone check my work/teach me proper methods if I'm wrong? Thanks.

How do I find the probabilty density function of a variable y being y=ab, knowing the probabilty density functions of both a and b? I know how to use the method to calculate it for a/b - which gives 1/pi*(a²/b²+1) - using variable substitution and the jacobian matrix and determinant, but which...

I drew an illustration to make this easier: Point P is where I wish to find the magnetic flux density H. Given the Biot-Savart formula: $$d\textbf{H} = \frac{I}{4\pi}\frac{d\textbf{l}\times\textbf{R}}{R^2}$$ I can let $$d\textbf{l} = \hat{z}dz$$ and $$\hat{z}dz\times\textbf{R} =...

Just calculating D1 (15km altitude plane) and D2 (7.5km altitude plane) turns out to; D1/D2 = 4*p1/p2 p being the air density at each height. How am I suppose to calculate p? We have had no such formulas, not to mention it depends on temprature etc. Doing a linear estimation will yield wrong...

V(ρ) = V_o*ln(ρ/0.0018)/ln(45/180) (Attached picture is where the unit vector of r is really ρ.) In cylindrical coordinates ∇V = ρ*dV/dρ + 0 + 0 ∇V =derivative[V_o*ln(ρ/0.0018)/1.386]dρ ∇V = V_o*0.0018/(1.386*ρ) E = V_o*0.0012987/ρ Work = 0.5∫∫∫εE•E dv Bounds: 0.0018 to 0.00045 m D = εE =...

The textbook says ' A conducting sphere shell with radius R is charged until the magnitude of the electric field just outside its surface is E. Then the surface charge density is σ = ϵ0 * E. ' The textbook does show why. Can anybody explain for me?

In a standard kitchen-microwave magnetron, like all magnetrons, a cloud of electrons forms which whizzes around and generates GHz electric currents in an outer ring electrode. For such a standard kitchen appliance, 800W made with ferrite magnets, what is the typical volume and density of the...

Here is my work done for this problem, along with a diagram of the situation. I'm not worried so much about the arithmetic because our tests are only 50 min long so the problems they give us do not require heavy integration or calculus, but you need to know what goes where in the formula. That...

Is there a rule of thumb that once a semiconductor's intrinsic carrier density reaches 10^15 cm^-3, that the semiconductor cannot effectively be used to perform useful operations?