Density Definition and 1000 Threads

Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below? However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an...

For the dimensions of a right cylinder, I am given three significant digits for the diameter (17.4 mm) and the height (50.3 mm). The formula for the volume of a right cylinder is V = Pi x r^2 x h, which would lead here to Pi x (17.4 mm / 2)^2 x 50.3 mm = 11,960.69354 mm^3 before rounding to 3...

My physics background is weak. My search found lots of ## E \times B ## and ## E^2 + B^2##, often associated with ## \mu_0 ## and ## \epsilon_0 ##, but never divided by ## 4 \pi ## and ## 8 \pi ##, respectively. Could someone provide a reference? Or a derivation? Thanks.

I just want to be certain, i think the inequality indicated is not correct...ought to be less than. Kindly confirm...This is a textbook literature.

[Mentors' note: moved from technical forums so no template] Hi All, Working on a lab write-up, and I need background equations to support the reasoning for my experiment. To outline briefly, two-part experiment, first part was finding the ideal pressure for a basketball, where I inflated it...

$$\phi_E=\dfrac{Q_{\textrm{enclosed}}}{\varepsilon_0}\Rightarrow Q_{\textrm{enclosed}}=9,6\cdot 10^{-7}\, \textrm{C}$$ $$Q_{\textrm{enclosed}}=\sigma S=\sigma \pi R^2\Rightarrow \sigma =\dfrac{Q_{\textrm{enclosed}}}{\pi (0,1^2)}=3,04\cdot 10^{-5}\, \textrm{C}/\textrm{m}^2$$ I have a lot of...

Increases in global temperature change affect the tree line and presumably comfortable habitability via temperature, and average air pressure associated with weather patterns. That's not what I mean. I'm thinking a 1/50 increase in kelvin temperature might increase the scale height of Earth's...

Hey, I have a really short question about electrostatics. The boundary conditions are : \mathbf{E}^{\perp }_{above} - \mathbf{E}^{\perp}_{below} = -\frac{\sigma}{\varepsilon_{0}}\mathbf{\hat{n}} , \mathbf{E}^{\parallel }_{above} = \mathbf{E}^{\parallel}_{below}. My question is what is...

I have to prove three equations above. For first two equations, I've been thought and made reasonable answer by using a definition of the electricfield. However, for third, I can't use a definition of a magnetic field due to the cross product Like J_2 X J_1 X (r_2 - r_1). I think three of 'em...

Hi all, At my workplace we have a waste stream that includes both natural and synthetic corks. The synthetic corks we can further process, so the natural corks have to be selected out. We have two Polish workers who are able to do this just by sight, 8 hours a day. However, we tried to put...

I recently encountered this problem on a test where the solution for the above problem was given as follows: $$F= \frac{Gm_1m_2} {r^2} $$ (1) but $$ m=\frac{4}{3}\pi R^3 $$ substituting in equation (1) $$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2} $$ where r=radii of the two spheres m=mass...

In an article written by Richard Rollleigh, published in 2010 entitled The Double Slit Experiment and Quantum Mechanics, he argues as follows: "For something to be predictable, it must be a consistent measurement result. The positions at which individual particles land on the screen are not...

Aerosol particles with an average diameter of 5 μm and a density of 1000 kg / m3 are spread to a room with a floor area of 20 m2 and a height of 3.5 m. How long does it take for all 5 μm particles to settle on the floor (dry deposition)? The answer should be 1 hour and 20 minutes.

I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know the probability density function and not the intensity function. I prefer not to have references...

Hi, I have a dialectric cube and inside the center of the cube I have a part where we have Introduced evenly electrons. I have to find the polarization charge density in the 3 regions. I know outside the cube is the vacuum, thus ##\vec{P} = 0## and inside the dialectric (non charged part)...

Hey! :giggle: For $n \in \mathbb{N}$ we consider the statistical product model $(X ,(P_{\theta})_{\theta\in\Theta})$ with $X = (0,\infty)^n$, $\Theta = (0,\infty)$ and densities $f_{\theta}(x_i) = \frac{1}{\theta} \textbf{1}_{(0,\theta)}(x_i)$ for all $x_i \in (0,\infty)$, $\theta \in...

Howdy partners! I am currently doing some project on Klt40s neutronic simulation (you might have heard of Akademik Lomonosov, the floating npp). But I have encountered a problem with fuel density. The only info that i got that "uranium density IN FUEL MEAT/KERNEL" is 4.5 g/cm3. The Fuel is...

I have doubts about the wording of the exercise: (1) energy density is ##u=\varepsilon_0 (cB)^2## but since the question asks for mean energy density should I perhaps average over ##cos^2 (\omega t)## (there due to the ##B^2##) and thus use ##<u>=\frac{1}{2}\varepsilon_0 (cB)^2##? (2) it seems...

If I want to carry 10 A through an 8 AWG wire, I understand that there will be a specific magnetic field around the wire which will decrease as I move outward from the wire radially. Let's consider the center of that wire as coordinates (x,y)=(0,0). An object located at (0,10) would see a...

Hydrogen production rate is typically measured in current density, but what is the area in which the current is divided by to find such a value?

Hi Pfs , happy new year. I wonder if there is a problem with the manner i see density matrices: I use to consider them without a statistical point of view , just like i do with Hilbert vectors. no more no less. So the points on the Block sphere are only pecular points of those which are inside...

Mathematically, you can convert between a power spectral density (PSD) and the modified allan variance as follows: $$\sigma_y^2 (\tau) = \int_0^{\infty} \frac{G_\nu(f)}{\nu^2} \times 32 \frac{(\sin(\pi f \tau/2))^4 \times |\sin(\pi f \tau)|^2}{(\pi \tau f)^4} df$$ I was wondering if anyone knew...

My general understanding of electric flux density is 'electric flux per unit area'. This gives the SI unit N/C. But According the formula of electric flux density, D=eplison*E, the SI unit is C/m^2. How come the dimension in both cases not matching if both are true?

Hello all. I am studying stat mech from Pathria's book. It says a system is completely described by all positions and momenta of all the N particles. This maybe represented by a single point in 6N-D gamma space. So, each point is a (micro)state. Now if we restrict the system (N,V,E to E+ΔE)...

There are some question involving the statement. One of them is about the charge density in S' frame. It asks to calc it. I thought that i could calculate the electric field in the referencial frame S' and, then, use the formula $$ E = \lambda / 2 \pi \epsilon l $$ In that way, i would obtain...

to solve a) I used The equation of hydrostatic equilibrium $$ \frac{d P}{d r} = - \rho \frac{GM}{r^2} \iff dP = - \rho \frac{GM}{r^2}dr \Longrightarrow \int_{P_c}^0 dP = - \int_0^R \rho \frac{GM}{r^2} dr $$ I replaced M as ## \rho V ## and then I integrated both the left and right-hand sides and...

hi guys our professor asked us to confirm the units of volume charge density ρ and also the surface charge density σ of a dielectric material given by $$ \rho = \frac{-1}{4\pi k} \vec{E}\cdot\;grad(k) $$ $$ \sigma= \frac{-(k-1)}{4\pi} \vec{E_{1}}\cdot\;\vec{n} $$ I am somehow confused about the...

Question: Relevant Equations: My attempt: Could someone please confirm my solution?

suppose that elecrons are in a state described by a diagonal density matrix for their spin (we are not interested in their spatial matrix). They are used in the double slit experiment. will we get fringes. I ask the question because when Bob ans Alice share pairs of electrons (the total spin of...

In the following pdf I tried to calculate the density of states of free electrons and phonons. First, I found the free electron DOS in 1D, it turns to be proportional to (energy)^(-1/2) and in 2D it is constant. However, I am not sure I found the DOS for phonons in the second part of the...

Hello. Firstly, I've calculated the density of Kr ( = 3.74 g/dm3), and I know that the p (fluid) = ρ * h * g. And then I've used the following equation: p1*V1 = p2*V2, and therefore: p1*V1 = ρ * h * g * (m/ρ) => p1*V1 = h * g * m. (h = 3.0153 m) Is that correct? Please, how could I calculate...

I have already calculated the polarisation that is $$ \mathbf{P} = \frac{\rho_f r}{2} \left( 1 - \frac{\epsilon_0}{\epsilon} \right) \hat{r} . $$ I tried to use the following formulas to calculate the density bound charges. For the surface bound charge I got: $$ \sigma_{b1} = \mathbf{P} \cdot...

Somehow this answer is incorrect , but i realize that even numbers are hipothetical , 45 coulumbs is too much charge , what is wrong in my calculations?

Hello, I wonder if you could give me some advice to how solve this question. What I was thinking to solve it was to determine J by using Ohms law, ## \vec J = \sigma_{\alpha} \vec E ## I already determined the E field for for the sphere, I got it from a) ("a)" was to determined all the bound...

[I've solved b, but can't figure out a for the life of me. I have a couple of attempts, but it's just nonsense, it's like I've short circuited.]

Hi, I was trying to solve the attached problem which shows its solution as well. I cannot understand how and where they are getting the equations 3.69 and 3.69A from. Are they substituting the values of θ₁ and θ₂ into Expression 1 after performing the differentiation to get equations 3.70 and...

(I must confess before I can begin that I found this problem difficult to understand, for reasons I will make clear below. I know it appears simple.) Attempt : Let me begin by drawing the problem situation alongside, to the best I understand. We can see that the in both cases (i) or (ii), the...

This doubt is confusing to me. I know it's something to do with conductors and insulators, but cannot explain. Conductors have mobile/free electrons unlike insulators. Having free electrons doesn't seem to explain this difference of charge distributions.

Guys I have Problems with this task The arrangement consists of a point charge Q at a distance (x0, y0,0) from the origin and two perfectly conductive surfaces in the (x, z) and (y, z) plane a) Mathematical description of the space charge density p of the original and mirror charge using the...

Phi= int(E.da) through a surface S is a measure of “number of field lines” passing through S. I put this in quotes because of course we can only draw a representative sample of field lines. The total number would be infinite. But for a given sampling rate the flux is proportional to the number...

Okay, so I tried thinking of this as like a simple balancing of equations. There's an infinite sheet of charge on the left and a conductor on the right with some charge already on it. My thought process was that the side nearer to the charged sheet would have 4.7 more μC/m2 than the far side...

Hi, The problem I am working on requires me to work out the the pressure on the outer conductor of a coaxial cable due to the current on the inner one. This cable carries a dc current of 5000 Amps on the inner wire of radius 2 cm. The outer cylindrical wire of radius 5cm carries the return...

In the 7th edition of the book "Elements of Electromagnetics by Matthew N. O. Sadiku" On page 190 the author goes on to say: "We now consider the case in which the dielectric region contains free charge. If ##\rho_v## is the volume density of free charge, the total volume charge density...

Hi. Suppose I have a state ##\left | \psi (0)\right >=\sum_m C_m \left | m\right >## evolving as $$\left | \psi (0+dz)\right>=\left | \psi (0)\right >+dz \sum_iD_i\left | i\right >=\sum_m C_m \left | m\right >+dz \sum_iD_i\left | i\right >=\sum_m( C_m+dz D_m)\left |m\right >.$$ Then the density...

I'm trying to show that the determinant ##g \equiv \det(g_{ij})## of the metric tensor is a tensor density. Therefore, in order to do that, I need to show that the determinant of the metric tensor in the new basis, ##g'##, would be given by...

Hello Forum, I am attempting to understand what causes pixelation when a bitmap (jpg, png, etc.) image is enlarged. Bitmap images have a resolution indicated as the number of pixels along the width and height of the image itself. On the other hand, computer monitors also have a physical...

Is the following a correct demonstration that quantum mechanics can be done in a real vector space? If you simply stack the entries of density matrices into a column vector, then the expression ##\textrm{Tr}(AB^\dagger)## is the same as the dot product in a complex vector space (Frobenius inner...

Hi All I am currently doing Master in data science. I came across the function PDF probability density function which is used to find cumulative probability(range) of a continuous random variable. The PDF probability density function is plotted against probability density in y-axis and...

Can the energy-momentum tensor of matter and energy be cast in terms of energy density of matter and energy, similar to how the energy-momentum tensor of vacuum energy can be cast in terms of the energy density of vacuum energy?