Surface Definition and 1000 Threads

Computing the Laplacian of ##(\frac{1}{|\vec{x}|})## in spherical coordinates I get 0 everywhere except at 0. Now I want integrate the Laplacian over a spherical surface that encloses the origin. I do this using Gauss's divergence theorem, i.e $$ \iint_S \vec{F}.\vec{dA} = \iiint_V \nabla . F...

I have some questions about Cauchy surfaces (not Cauchy horizons). I know that a Cauchy surface cannot be timelike, and can be spacelike. What about null? Can a Cauchy surface be lightlike? Also, do Cauchy surfaces need to “cover” the entire manifold in some sense? The definitions that I...

Hello , In the system below there is a mode i am trying to couple. at weak coupling I get a certain surface current responce and in stronger coupling I have different responce as shown below. How can I see from the surface currents where can i improve the coupling in my model?

This is the description of the thought experiment. There are two plates forming a parallel plate capacitor. Both plates are rectangular but one is large and long and the other is much smaller. Both are "charged up", the difference is that the smaller plate has surface charge across it's full...

Source: https://tutorial.math.lamar.edu/Problems/CalcIII/SurfIntVectorField.aspx Alright so my confusion lies in the following step: Consider the side x = 0. Okay, from the formula (I am just going to insert an image here) Okay, so gradient of f would just be <1, 0, 0>, which is simply i...

I am reading Purcell's Electricity and Magnetism and am getting confused on equation 5.22. It seems to me they are using relativistic velocity addition for u' which is u'=(u-v)/(1-uv/c^2), but aren't we solving for the velocity of the electrons in the test charge's frame of reference, so should...

Evening all, im not exactly sure where this lies in the prefix, so apologies if it is higher than that. I am trying to figure out a device that uses fan vacuum and suction seal, and a little bit of ground effect with a fan to adhere to objects, I'm by no means a learned man, and i was...

I first thought of imaging techniques, because the setup reminded me of it, but i have only ever seen those of electrostatics. If i for example add a current in the opposite direction and with the opposite heigth of the surface the fields dont cancel out at the surface, i think. What is the best...

I'm a little thrown off with material I'm going through right now. I already covered the whole "area under the curve" and using that to determine the volume of a given equation, but I'm confused now as to why calculating the surface area has a different method with ds? For example, say there...

A solid ball of radius R, density ρ, and Young’s modulus Y rests on a hard table. Because of its weight, it deforms slightly, so that the area in contact with the table is a circle of radius r. Estimate r, assuming that it is much smaller than R. I have no issues understanding the...

Is it true that hydrogen and oxygen atoms on the surface of diamond make it have such a low coefficient of friction?

Derive formula for surface brightness The formula in question we wanna derive is: S(mag/arcsec^2) = M⊙ + 21.572 -2.5 log_{10} S(L⊙/pc^2). Best regards.

We have 2 infinite cylinders, need to find out which shape will equipotential surface be in 3D.

I'm not sure this is a differential geometry question, but I think it is. In general when we have a hypersurface(or in case of 3D space just a surface) it is defined with an equation ##f(x^a)=0## for some function ##f##. Then the normal vector is the gradient of this function, if we want an...

Is it just sqrt2?

I would think the black painted surface is

Hello PhysicsForums! Here is my attempt at a solution for the problem stated above: Where m1 and m2 are the masses Where Ff1 and Ff2 are friction for each mass Where a1 and a2 is the resulting acceleration Where S is the fore of the wire (threadforce) Where FN is the normal force The answear...

Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems. Have a wonderful day, again thank you for checking this post out!

Hi togehter, this may be an easy one for most, but I'm really struggling with imagining the process. Suppose we have a compressed air vessel that is half filled with water. The pressure in the vessel drops from 10 bar to atmospheric pressure within a few seconds. How does the water surface...

This is the problem and my answer below it. my friends said it's 250 N and I say it's 100 N based on what I solved what am I missing ?? my try:

The answer to the first question should be a sphere since for very large distances the multiple charges will act as a point charge. 1(a) is correct answer. For the second question, I find it slightly vague. How can equipotential surface be zero, may be it's asking for the potential of...

Hi all, While calculating the surface area for an object, I was told the below statement. However, I am not sure is this correct, please can someone help me to explain this with an example? Is the below statement always true? The surface area % increase should be in line or less than the %...

My Work so far: So there is a Force F applied to the right and since we have a no slipping condition we have a static friction force fs to the left. So the only thing that can move the center of mass (cm) of the yoyo is rotation. F would lead to a ccw rotation and fs to a clockwise rotation...

Hey everyone. Let's say you have a tall tree. say, 10 m tall. Take a cubic cell 1mm in dimensions. Suppose the cell is at 1 m high in the center of the trunk of the tree. What are the forces acting on the cell? let's say tree cell's mass is t grams. its weight is F= ma = t (9.8) = 9.8 t...

Hi everyone, I'm trying to set up a surface neutron source on the surface of a cylinder defined as a macrobody (RCC) and used also to define cell of the system. My aim is setting up a surface source where I'd like to give a specific spectrum (and DIR) at each surface defining the cylinder...

In the low temperature limit ##\mu \approx E_F## and the Fermi-Dirac distribution is ##n(E) \approx g(E)/(e^{\beta(E-E_F)}+1)##. An escaping electron contributes ##\Delta j_z = -ev_z = -ep_z/m## to the current density. How can I calculate the rate that electrons escape at? I can't see how to...

I am struggling with how to go about this; in particular, I'm not sure I understand what state is being alluded to when Ballentine says "For an electron that approaches the surface from the interior, with momentum ##\hbar k## in the positive ##x## direction, calculate the probability that it...

Hello everyone. First post! I am struggling to understand an issue in our (histology) lab. We use large downdraft tables which extract the noxious substances we use, mainly formaldehyde, while we process surgical samples. These tables have a steel cover with lots of holes about 5mm diameter...

The correct answer to this problem is: ##\sigma = \varepsilon_0E\frac{\varepsilon-1}{\varepsilon}## Here is my attempt to solve it, please tell me what is my mistake? ##E_{in} = E_{out} - E_{ind}## ##E_{ind} = E_{out} - E_{in}## ##E_{in} = \frac{E_{out}}{\varepsilon}## ##E_{ind} = E_{out} -...

Also referring to the post by @Kostik plus answers, I'm wondering about surface charges of neutral solids such as metals or carbon, for example. I only want to discuss large scale effects so that the solid can be treated as continuous. The atomic structure is averaged out. I also assume that...

So I was reading about frequency selective surface radome, basically this is the kind of cover over the antenna which allow a certain frequency wave to pass through and reflect wave at any other frequencies. What I don't understand is the reflection vs transmission coefficient chart. So as I...

I need help with part b. My solution: Have I done it right?

Desired output similar to image, but without the objects and with better wave interference: I tried plugging the following into wolfram (I specifically want the values to be adjustable): plot z= H*e^(-m*sqrt((x-a)^2+(y-b)^2))*sin(k*(x-a)+k*(y-b) -w*t) +...

I recently conducted a physics lab to measure the surface resistivity of a conductive sheet of a paper with a carbon filler. The theoretical Rs is approx. 5,000 Ω/☐ for this paper and yet we have calculated two Rs values: Rs when Varying Length and holding Width = 10100 +/- 83.07 Ω/☐ Rs when...

Hi, I have a question concerning surface tallies like F1 and F2. You have to provide a surface for them. Since, surfaces are defined as infinite (infinitely long cylinders, infinitely extended planes) how can you write the surface tally of a cell? What are the actual tally surfaces for F1 anf...

Here's my attempt at a solution, but when I plug it in, it gives me a power ten error. I don't really understand what I'm doing wrong here. I think all my variables are in the correct units and it asks for my answer to be in μC/m2. Any help is much appreciated.

I want to build a mini chemical cabinet to try to eliminate odors in my garage as my wife thinks the car interior now smells. The chemical resistant rubber strip sealant is crazy expensive, but as the intended use will just be fumes with no actual chemical or fuel contact to the seals, can I use...

1.If the thickness of soap water surface decrease, whereas the concentration remain the same, how will the surface tension change? 2. If the membrane of soap water start to evaporate, its thickness become thinner and it’s concentration increase, How will the surface tension change? Thank you!

I got these values but I wanted to make sure I was doing it the correct way a) 0.548 J/g for system of 1 µm cubes b) 9.131 x 10^19 J/g for system of 1 nm cubes c) 273.890 J/g for system of 1 nm radius spheres

For this problem, The solution is, However why is ## r = (208)^{1/3}(1.20 \times 10^{-15} m)## Many thanks!

how can I go about finding the surface absorptance of a material if I'm not given the radiant emittance of the non- black body?

My question is on how did they determine the limits of integration i.e ##2## and ##3## as highlighted? Thanks

Roughly, how much force does it take to make 1 mm surface bump of diameter 16 mm circle area out of 1 mm thick steel plate of far larger area (e.g. a muscled hand pounding it laid over the base with 16 mm dia. hole by M16 bolt medium is viable enough) ?

I usually think of a sphere as the set of all points ##P_x##, that have the identical distance r to some point ##C## which is the center of the sphere. I calculate the surface area ##A## of the sphere as $$A=4 \pi (C P_x)^2$$ However, what happens if I think of the distance between the points C...

What have mistakes/wrong assumption have I made in solving this question? I tried to solve the problem this way N.B. I assume that the j hat direction is up.

The doubt is about this question. Which the answer is They say that all the forces are pulling forces? How is this the case? How would this setup even work? I don't think block 2 could pull the rod.

Greetings all, I'm new here and hope I'm asking this in the correct thread. So, the question is; where you have a vacuum created by a "flow through" liquid witin a large diameter container exerting suction force upon a smaller diameter input tube submerged in a liquid, does the surface area of...

I'm supposed to do the surface integral on A by using spherical coordinates. $$A = (rsin\theta cos\phi, rsin\theta sin\phi, rcos\theta)/r^{3/2}$$ $$dS = h_{\theta}h_{\phi} d_{\theta}d_{\phi} = r^2sin\theta d_{\theta}d_{\phi}$$ Now I'm trying to do $$\iint A dS = (rsin\theta cos\phi, rsin\theta...

I mean you could buy a mirror or silicon wafer but they give say 0.5 nm or 5nm 'roughness' which I suspect is the mean average roughness but this doesn't rule out a high "bump" way above the mean average such that for example 1 million bumps of 1 nm and just one of 5 will result in...