Density Definition and 1000 Threads

https://www.quora.com/How-can-I-find-the-probability-density-function-of-a-continuous-random-variable-in-a-given-problem/answer/Maxime-Denis-2 How can I find the probability density function of a continuous random variable in a given problem? A mass m swings at the end of a rope (of length L)...

Hi all This is not a homework question but something work related which I am having difficulty understanding which I was hoping someone from the community could help me with. I am trying to understand how to interpret & create the probability density function plot from a set of data. For...

Homework Statement Let X, Y, and Z have the joint probability density function f(x,y,z) = kxy2z for 0 < x, y < 1, and 0 < z < 2 (it is defined to be 0 elsewhere). Find k. Homework Equations Not sure how to type this in bbcode but: Integrate f(x,y,z) = kxy2z over the ranges of x (zero to...

Hi. I know how to use Gauss' Law to find the electric field in- and outside a homogeneously charged sphere. But say I wanted to compute this directly via integration, how would I evaluate the integral...

I am trying to formulate the Current Density for a Loop of wire with a diameter,d, current,I, and an cross-sectional Area of the wire ##\pi(d/2)^2##. With spherical coordinates (radial, azimuthal, polar) ##\bar j## = ##\frac{I}{\pi(d/2)^2}*cos \theta *sin \phi \hat x##...

Homework Statement Hi there, I am designing a heat exchanger and I am really struggling to find out how to fairly accurately estimate the density, viscosity and thermal conductivity of a gaseous mixture at ~~20bar. There is 8 components in the mixture: methane, ethane, ethene, ethlyene oxide...

Hi folks, here's a thought/conceptual question I've been wondering about. What is the maximum theoretical specific energy (IE Joules/kg or equivalent) for energy stored in the electric field of a capacitor? I know the energy stored in a capacitor is given by U=C V^2/2, and the mass of the system...

It has been a long time since I have worked with this and I need help just starting out. The problem involves the density of a liquid, the density of a solid, and the height where the solid will be released in the liquid, gravitational force, and the time it takes to reach the top of the...

Can Lagrangian densities be constructed from the physics and then derive equations of motion from them? As it seems now, from my reading and a course I took, that the equations of motion are known (i.e. the Klein-Gordon and Dirac Equation) and then from them the Lagrangian density can be...

Homework Statement Consider the parallel plate capacitor(no figure). The capacitor plates have a separation distance d in the z-direction. The volume charge density is given by ρ_v. Find v(z).Homework Equations ρ_v = ρ_o*sin(pi*z/2*d) The Attempt at a Solution [/B] ∫(ρ_vdz) =...

I want a QM textbook which introduces detail knowledge of density matrix and trace (i.e. the average), who can recommend one for me? Thank you.

Homework Statement A uniform U-tube is partially filled with water (ρH20 = 1000 kg/m3). Oil, of density 750 kg/m3, is poured into the right arm until the water level in the left arm rises 30 mm. The length of the oil column is then: (Answer: 40mm) Homework Equations P = pgh Pressure = density...

Homework Statement "In January 2006, astronomers reported the discovery of a planet comparable in size to the Earth orbiting another star and having a mass of about 5.5 times the Earth's mass (5.97 x 10^24 kg). It is believed to consist of a mixture of rock and ice, similar to Neptune. If this...

Hello Everyone, Could anyone please explain the difference between the conduction current density (J=σE) and the convection current density (J=ρvd)? I really appreciate any examples or applications to further elaborate these two theories. Note: vd is the particles' average drift velocity...

Hi. 1)In relativity theory mass is not additive so we cannot divide it to contributions from different parts in a system. In this sense "mass density" volume integration of which is mass is a false idea, isn't it ? 2)In a system that is a tiny tiny fraction of space would contain only one or...

Hello, I've been watching too much anime. I know that isn't the best way to ask a question scientific in nature, but visualizing bizarre situations is one of the best ways to come up with interesting questions. Anyways, in order to break a rock by compressing it with your hands, you would need...

Hi I am trying to understand the figure 2 I have attached to this post. From text: Ok, I get that the air-gap flux density varies in a sinusoidal manner, because the air gap length is not constant i.e. non-constant reluctance and hence non-constant magnetic flux density. What I do not...

Homework Statement Consider a ring of radius R placed on the xy-plane with its center at the origin. A total charge of Q is uniformly distributed on the ring. a) Express the volume charge density of this configuration ρ(s,Φ,z) in cylindrical coordinates. b) Express the volume charge density of...

Homework Statement A point charge ##q = −5.0\times 10^{−12} C## is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is...

Homework Statement Consider a glass sphere completely filled with water except for a small air bubble at 1 atmosphere. The sphere is accelerating to the right. What is the pressure at the center of the sphere? Let Pe = Atmospheric pressure r = radius of sphere pw = density of water a =...

Homework Statement An infinitely long line of charge has linear charge density ##λ=4.00_{10^{−12}} \frac{C}{m}##. A proton (mass ##m_p=1.67_{10^{-27}}kg##, charge ##e=1.602_{10^{-19}}C##) is ##r_a=0.18m## from the line and moving directly toward the line at ##v=1000\frac{m}{s}##. Homework...

Homework Statement Taken from Purcell Problem 1.33 Consider the electric field of two protons a distance b apart. The potential energy of the system ought to be given by U=∫E2dv. Let E1 be the field of one particle alone and E2 that of the other. Evaluate ε0∫E1⋅E2dv. Set one of the protons...

I'm not sure I understand how to correctly scale flux density with redshift. That is, if I observe say 10 Jy at my observing frequency coming from a source at z = 0.3, how can I estimate the flux density I would expect from the same source at z=2? From what I understand, the final scaling is...

Homework Statement "A straight, nonconducting plastic wire ##x=9.50_{10^{-2}}m## long carries a charge density of ##λ=1.3_{10^{-7}} C/m## distributed uniformly along its length. It is lying on a horizontal tabletop. If the wire is now bent into a circle lying flat on the table, find the...

$\textsf{A thin rectangular plate, represented by a region $R$ in the xy-plane}\\$ $\textsf{has a density given by the function p(x,y);}\\$ $\textsf{This function gives the area density in units such as $g/cm^2$}\\$ $\textsf{The mass of the plate is $\displaystyle\iint\limits_{R}p(x,y)dA$}\\$...

The probability density of the dirac spinor is known to be ∑(Ψ)2 and I know how it is derived. However, I'm just wondering why it should be positive definite. Since the lower two components represent antiparticles, so shouldn't the probability density contribution of those two components be...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Corollary 2.1.39/Exercise 2.1.40 ... Corollary 2.1.39/Exercise 2.1.40 reads as...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with an aspect of the proof of Theorem 2.1.38 ... Theorem 2.1.38 reads as...

Flux density of a magnet is about how many T? In an experiment, I obtained the number 227.6 T. Is this a sensible value for a small (5cm long) bar magnet? Thank you~

Homework Statement Homework EquationsThe Attempt at a Solution ##\rho = b r \\E =\frac { k r^2} {4ε_0} \\ p ∝ E^a \\E \left ( r=d \right ) = \frac { k d^2} {4ε_0} \\ p = q d \\ d ∝ d^{2a} \\a = ½ \\p ∝ √E ## PART B ##\rho ∝ r^n \\E ∝r^{n+1} \\ p ∝ E^a \\d ∝d ^{{n+1}a} \\## For eq. 4.1 to...

Currently, I am reading this article which introduces electromagnetism. It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$ The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory...

is there any way to derive p=rho/3 from 4 vector or stress-energy tensor?

Hello all, I have a petri dish 8.7 cm in diameter filled with 20 mL of TSB media. I have set up a .7mm graphite at the 0cm mark of the diamter and measured current at 4.6Volts over the entire distance of the petri dish (8.7cm) with .5 cm step sizes. For example: When the probes are 1cm apart I...

Homework Statement In a configuration having axial symmetry about the z axis, a line current I flows in the −z direction along the z axis. This current is returned at the radii a and b, where there are uniform surface current densities Kza and Kzb , respectively. The current density is zero in...

If we have a bottle with a fluid A of X density, and in the bottom of this bottle it magically spawns the same amount of fluid B with X/2 density, fluid B should rise in fluid A until they both change positions and fluid B floats in A. Wich property of the fluids are the ones that determinates...

Suppose we have a fan/blower that is working at sea level. It has a certain RPM against a specific voltage and current. We all know that. Now, that fan/blower has been brought to the top of a mountain where air is sufficiently less dense and the same voltage and current has been applied to the...

For a divergent paraxial field like $$E = E_0 e^{-\frac{r^{2}}{w(z)^{2}}} e^{-i(kz - tan^{-1}(\frac{z}{z_{0}}))}$$ What is the direction of the momentum density of the E-field. I have two competing feelings about it. 1) The momentum density should be parallel to the Poynting vector, and since...

Homework Statement In my experimental setup I have a purpose built small aluminium tube that has a black layer on the inside to mimic a blackbody. The tube is heated so the inside emits as a blackbody. A separate temperature sensor attached to the tube gives the temperature of the tube. I...

Hello All I was wondering if someone could help explain what the probability density function tells you. I am trying to learn about surveying and the PDF keeps cropping up and I do not fully understand it. For example I have:- measured a single angle 15 times calculated my Standard Deviation...

i work on phononic crystals and i want to find solids with diffrent sound velocities and mass density in diffrent temprature i can just find BST but i need more matherials please help me my friends best regards

Homework Statement There are n isolated condutoctors in space: Sum of charge of all conductors is positive. Show that surface density is postivie everywhere on at least one of conductors Homework Equations Using induction The Attempt at a Solution -It's clear that if we have one conductor...

Hello, Let's suppose we have a two dimensional lattice which is periodic along certain direction, say x-direction, allowing us to define a quasi momentum k_x. The lattice is not periodic along the y-direction (perpendicular to x-direction). Therefore, we are able to obtain the band structure...

Hi, I have been reading about diborane (B2H6, a gas at standard conditions) and while the sources provide different density values (!), as in 1.2475 g/L at standard conditions, or 1.18 g/L at 15ºC and 1.216 g/L at 25ºC (sounds crazy?), all of them are lower than dry or moist air at the same...

Without knowing whether WIMPs or axions or something else are what dark matter is composed of, can we speculate about the vacuum density creating only normal matter, and by what mechanism?

With NASA defining this equilibrium density at 9.9 x 10<30 gm/cm3, how can an increasingly expanding universe maintain a steady density as it expands?

Homework Statement Hi, I am doing physics lab on finding coefficient viscosity of fluids and how it changes by temperature by dropping a marble into fluids, finding terminal velocity, then using stoke's law to find viscosity. (using density of fluid, sphere, sphere diameter etc). The equation...

Hello! I am a bit confused about the interpretation of probability density in QFT. Let's say we have the Klein-Gordon equation. I understand that this is the field equation for a spin-0 charged particle. So if we find a solution ##\phi(x)## of the Klein-Gordon equation, as far as I understand...

Homework Statement A positively charged nonconducting solid sphere of radius R has a nonuniform volume charge density given by ρ0 for r≤R/2 and given by 2ρ0(1−r/R) for R/2 ≤r≤R, where r is the radial distance from the sphere center.Part A Determine the charge q on the sphere in terms of ρ0 and...

Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...

The density of ice is 920 kg/m3. Now let's calculate. m = 269 000 000 000 000 kg p = 920 kg/m3 ----------------------------- v=? V=m/p V=269 000 000 000 000 kg / 920 kg/m3 V = 292 391 304 347 m3 = 292 391 304.347 km3 v > 269 km3 *NOTE* I made a mistake in the title. I meant to write 269 km3...