Surface Definition and 1000 Threads

Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?

I would think that a force due to surface tension would act upwards on the plate and not downward, as shown in the diagram I have come up with. The surface of water would act as a stretched membrane and therefore there would be a surface tension on water surface in contact with the bottom of the...

I think in the explanation below a very small element of the liquid at the line of contact between the horizontal solid surface, air outside the liquid and the liquid itself is being taken, and forces acting on such a small element are being shown. This very small element is to the left of shown...

The solution said that Average power= net change in energy/time, but why is that true? If you have a different way of solving it, it would be helpful too

The picture above shows the integral that needs to be evaluated, and the associated picture ## \cos\alpha ## can be obtained via the law of cosines. I'm simply confused as to where the ##\cos\alpha ## comes from in the first place. I just don't see why ##\cos\alpha ## is necessary in this...

I read a paper about coherent surface plasmon amplification by free electron pumping in an article a few days ago. It seems to work as some kind of free electron laser-like light source, and I wonder how high the energy of photons can go in this way. Also I read in another paper about...

Can a photon ever be motionless relative to the earth's surface? Did it accelerate from 0 mps to 186,000 mps?

I have gel which has a specific gravity of about 0.8 and a stated viscosity of 25000 mm2/S (whatever that means). It's thicker than honey. It just sits there with an uneven top surface. About 20cc are in a container and I want to flatten the surface. The best I can do is to shake the container...

Dear friends, I will be grateful if anyone can help me I study electromagnetic scattering by rough surfaces for a certain case. Each rough surface can be specified with the statistical parameters sigma (σ) and correlation length (lc). while writing my manuscript I drew a schematic...

Hello, I learned recently about alveolar surface tension, and the explanation provided in the course was not satisfactory, it said that it is due to the force that pushes water molecules of the outer layer to the inner layers, I don't understand why this force that pushes water toward the cell...

a.) The scale length of the disk is the length over which the surface density of stars decreases by a factor of e. In this case, the surface density decreases by a factor of 10 over a distance of 9 kpc, so the scale length is 9 kpc. The surface density of stars at a radius of r from the center...

The problem that I immediately ran into was how I would calculate N without knowing Fmax. I didn't think the y-component of N would simply be the same magnitude as mg. After being stuck for a good while I even tested if it was, by dividing the magnitude of mg with cosθ, which of course ended up...

Suppose you have an infinite plane of charge. If the surface charge density is uniform, would the tangential electric force always be zero, even if it is not a conductor nor static? My thought process for this is that if you look at each point charge and draw the electric field lines, then at...

Hi I am looking to find the equation that determines the minimum (and if possible maximum that might damage the electrode) voltage that starts the electrolysis process for a given area of a graphite electrode in a brine solution medium (lets say 30%) at equilibrium state. Also how does the...

The definition of a Cauchy surface, as given in, for example, Wald Section 8.3, is "a closed achronal set ##\Sigma## for which ##D(\Sigma) = M##", i.e., every past and future causal curve (timelike or null) through any point in the entire spacetime intersects ##\Sigma##. The definition of...

According to my current understanding rolling friction rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and...

The vectorfield is $$A = grad \Phi$$ $$A = x^2 + y^2 + z^2 - (x^4 + y^4 + z^4 + 2x^2y^2 + 2x^2z^2 + 2y^2z^2)$$ The surface with maximum flux is the same as the volume of maximum divergence, thus: $$div A = 6 - 20(x^2 + y^2 + z^2)$$ This would suggest at the point 0,0,0 the flux is at maximum...

But the answer provided is ##\frac{15}{4} ## How is that? What is wrong in the above computation of answer?

A golf is launched at a speed v,f and launch angle, β,f. The slope of the green is equal to φ. At some point the ball is located on the rim of a hole. The side view (a) and overhead view (b) looks as in the attached image.According to the author of the [paper][2] "The Physics of Putting" the...

Evaluate the surface integral $\iint\limits_{\sum} f \cdot d\sigma $ where $ f(x,y,z) = x^2\hat{i} + xy\hat{j} + z\hat{k}$ and $\sum$ is the part of the plane 6x +3y +2z =6 with x ≥ 0, y ≥ 0, z ≥ 0 , with the outward unit normal n pointing in the positive z direction. My attempt to answer...

I'm studying oceanography and the author of the book that I'm currently reading stated that sea surface water is relatively constant during the day, changing very slowly during the year. He says "this is because almost all the energy received from the sun is used in the evaporation of water"...

The Hamiltonian of a particle of mass ##m## on the surface of a sphere of radius ##R## is ##H=\frac{L^2}{2mR^2}## where ##L## is the angular momentum operator. I want to solve the TISE ##\hat{H}\psi=E\psi## and in order to do that I rewrite ##L^2## in Schroedinger's representation in spherical...

I have a problem with this Hamiltonian: two identical particles of mass ##m## and spin half are constrained to move on the surface of a sphere of radius ##R##. Their Hamiltonian is ##H=\frac{1}{2}mR^2(L_1^2+L_2^2+\frac{1}{2}L_1L_2+\frac{1}{2}S_1S_2)##. By introducing the two operators...

Antarctica's only active volcano shows how CO2 allows volcanoes to form persistent lava lakes at the surface https://phys.org/news/2022-05-antarctica-volcano-co2-volcanoes-persistent.html

Greetings the solution is the following which I understand I do understand why the current orientation of the Path is positive regarding to stocks (the surface should remain to the left) but I don´t understand why the current N vector of the surface is positive regarding stockes theorem...

I am not very good at proofs. The only thing I have come up with is the following regularity. However, I am not sure how this can be related to the above problem. Given a sphere ##S_a## with a center ##C## and a diameter of ##a##. I can now construct a line segment ##b## with the endpoints...

This was a trivial question I had (which I posted here on the PF EM Forum: https://www.physicsforums.com/threads/bound-charges-polarisation-of-a-half-cone.1015308/). As I received no response on the above link I decided to post the same as a self formulated HW problem. Below I have attached an...

I have tried to solve the problem by setting as a condition that the electric field inside the conductor has to be 0, but in this way I have two unknowns (σ1 and σ2):

I will only care about the ##t## and ##x## coordinates so that ##(t, z, x, x_i) \rightarrow (t,x)##. The normal vector is given by, ##n^\mu = g^{\mu\nu} \partial_\nu S ## How do I calculate ##n^\mu## in terms of ##U## given that the surface is written in terms of ##t## and ##x##? Also, after...

I would like to use a pentaprism with some amount of magnification. The pentaprism will be used to reflect a real image at 90 degrees angle but I also want the reflected image to appear larger. The distance between the prism and the real image is about 70cm. The pentaprism has two reflecting...

For my project, I need water waves of all frequencies to move at the same speed. I read this article, but struggled to grasp some concepts. The key idea of the article is that a raindrop hitting a water surface basically creates a pulse containing all the frequencies, and since the water is very...

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...

Hi everyone! I'm pretty new in this forum, I found the topics here very relevant to my physics course. And here is my question: Given the following drawing, two infinite sheets (in y and z axis) of ideal conductive material. their thickness is infinitesimal (dx->0). The electric field is...

When I try to derive Gauss's law with a straight line of charge with density ##\lambda## through a cylindrical surface of length L and radius R, $$\vec E = \frac{\lambda*L}{4\pi\epsilon*r^2}$$ $$A = 2\pi*r*L$$ $$\vec E*A = \frac{\lambda *L^2}{2\epsilon*r} \neq \frac{q_{enc}}{\epsilon}$$ What am...

Below is an image to calculate the surface area of a sphere using dA. I can see how ##rcos\theta d\phi## works, but I don't understand how that side can't just be ##rd\phi## with a slanted circle representing the arc length. The second part I don't understand is why it is integrated from...

I am confused at this calculation of the electric flux through a trapezoidal surface. The flux in should equal the flux out. The flux in equals -E*A1 where A1 is the area of the bottom of the trapezoid. The flux out equals E*A2 where A2 is the area of the top of the trapezoid. But the two fluxes...

Hi all, I am reading this thesis and have two questions to section 5.1.5: https://rsl.yale.edu/sites/default/files/files/RSL_Theses/reagor-thesis-20151202.pdf First question is: Where did equation 5.19 come from? Second question is: If you look at this paper https://arxiv.org/pdf/1308.1743.pdf...

In a quantum mechanical exercise, I found the following Hamiltonian: Consider a particle of spin 1 constrained to move on the surface of a sphere of radius R with Hamiltonian ##H=\frac{\omega}{\hbar}L^2##. I knew that the Hamiltonian of a particle bound to move on the surface of a sphere was...

Suppose we leave an object on a non-sloping surface that rolls and moves forward without slipping. Does this object continue to move indefinitely?

What happens to the buoyant force at the surface of the water for an object? The buoyant force should be greater than the weight of the object if the object were to float up but once the object floats to the surface, there is no more acceleration upwards which means the buoyant force = weight of...

I am trying to find out what the smallest hole water will flow through. not a molecule of water, just water in general. Here is an example. I have a single walled cube that i 3d printed. When i put water in it, it leaks between the layer lines. I want to find out what the spacing between the...

[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...

If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...

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

I'm writing a paper on the movie realism of the A-team movie. The basic situation is that the guys are falling inside a tank with terminal velocity into a lake. I'm stumped on how to calculate the force that is created on impact, though I imagined it being done with some kind of pulse equation...

I am doing a University lab project where I measure positions of sunspots (using images from NASA's SDO) and use them to calculate the rotation of the Sun. Currently, all is going well: I have the angular velocity of several sunspots at varying heights. However, I want to be able to find the...

Energy required = ##\Delta E_p## $$\Delta E_p = -\frac{GMm}{R}+\frac{GMm}{2R}$$ $$=-\frac{1}{2} \frac{GMm}{R}$$ $$=-\frac{1}{2} \frac{GMm}{R^2} R$$ $$=-\frac{1}{2} 40R$$ $$=-20R$$ But the answer key is 40R. Where is my mistake? Thanks

Question: Equations: My attempt: Could someone confirm my answer please?