Surface Definition and 1000 Threads

A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called surface, sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface.
The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.

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  1. sagigever

    Experiment involving surface tension for water and alcohol

    I really have no idea how to approach this question, I was thinking write ##F=mg## but I am not sure if I can write that even though
  2. A

    Do Overlapping Feathers on Swifts Offer Insights for Aircraft Design?

    Do you thing swift birds(most aerodynamics birds; 10months in the air without landing,fastest birds in horizontal flapping flight -169km/h) have some benefits of overlaping feathers which gives rough surface? Can planes benefits from...
  3. D

    Using Surface Integrals, calculate the area that vanishes with this rising tide

    Please help to see whether it's correct to do in this way
  4. D

    Using a Surface Integral for Mathematical Analysis of the Area of an Island

    I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks
  5. sagigever

    Finding Percent of Water & Oil in a Mixture from Surface Tension

    I was looking for on the internet for a while without a success. If I know that the surface tension of pure oil is ##\gamma_o=A## and I know that the surface tension of pure water is ##\gamma_w=B## so if I have a mixture of water and oil with surface tension ##\gamma_m=C## am I able to know...
  6. Adesh

    I Why volume is conserved but not the surface area?

    A water drop of radius ##10^{-2}## m is broken into 1000 equal droplets. Calculate the gain in surface energy. Surface Tension of water is ##0.075 ~N/m##. So, for the solution of the above problem we need to know how much surface area (combining all 1000 droplets) have increased from the...
  7. E

    Surface tension and Young's contact angle

    I came across this diagram, the ##\gamma##'s are supposedly forces per unit length of the respective interfaces: It's not clear what these forces are acting on. ##\gamma_{SL}## and ##\gamma_{LG}## look like they could be acting on a small bit of water right at the end, but I have no idea what...
  8. Frigus

    Why is the net flux through a closed surface equal to zero?

    Suppose we have placed a cube in field which varies linearly with z axis so electric field magnitude on coordinates of face ABCD is clearly more than face EFGH and we know area of both faces are equal, So if we calculate flux then it would be non zero but it contradicts with the fact that...
  9. D

    I Partial Surface Area of a Tube

    Hi all, I hope this is the correct place to post this. Below is a section of a pipe. The pipe has a radius of 0.848 m. For this example, assume the pipe is buried below ground but a section of it remains exposed. The centre of the pipe is buried 0.590 mbelow the ground. If we assume the pipe...
  10. P

    I Do more impact craters always signify old age of a surface?

    I've learned that the surfaces of places like the moon and the surfaces on Mars corresponding to the Noachian period signify relatively old surfaces because weathering and erosion tend to make those cratered surfaces smooth. However, I heard a professor mention that this is also true for icy...
  11. F

    What happens to surface charges when conductors/dielectrics touch?

    When 2 conductors/dielectrics touch, will surface charges move away from their original conductor/dielectric to the other?
  12. H

    MHB Volume and surface area of "One World Trade Center"

    Hi to everyone, do you know the "One World Trade Center"? Well, I've to calculate two things about it: -The volume, according to its particular shape -The surface of the glass plates which cover the whole structure Searching on internet i found two dimensions: 1) Total height without...
  13. F

    I Any surface bounded by the same curve in Stokes' theorem

    In Stokes' theorem, the closed line integral of f=the surface integral of curl f on ANY surface bounded by the same curve. But in Gauss' theorem, the surface integral of f on a surface=the volume integral of div f on a unique volume bounded by the surface. A surface can only enclose 1 volume...
  14. sbrothy

    I Barrow black holes with fractal surface?

    This should maybe go in the Beyond The Standard Model forum but since it's a paper about quantum cosmology I'll put it here. Feel free to move it if it's too speculative but that's exactly my question. That is: if it is... Perusing "The Area of a Rough Black Hole" - -...
  15. R

    Does a square shaped line may have a circle shaped Gauss' surface

    Summary:: For finding the electric field at P in the photo below, may I select a gaussian surface circular? [Mentor Note -- thread moved to the schoolwork forums, so no Homework Template is shown]
  16. T

    I Area of an inclined surface with respect to the original surface

    Hi, I have a problem with inclined planes. The idea is to calculate the stress in an inclined plane of a bar under tension for which you need the surface. I have no idea how this surface is derived, though. In the attached file, you can see what I mean. For a rectangular cross-section, it's...
  17. S

    A Laser Ablation of a fused silica surface

    I read in couple of articles, like this one: https://link.springer.com/content/pdf/10.1007/BF00324203.pdf that regions of fused silica surface can be ablated by laser... I have two questions: 1- Why does the ablation occur? 2- does the ablation happens when the laser waist point is under the...
  18. S

    A Molecules Aggregating on a Surface that includes a Scratch

    View from above of fused silica chip. In the image is fused silica and the black line is burned fused silica caused by laser, when I cast droplet that contains molecules, never mind which kind of aggregation I tried different kinds of molecules, the aggregation is more preferably on the burned...
  19. A

    I Average of the B-field over a volume and surface integrals

    Purcell says that taking the surface integral of the magnetic field ##\textbf{B}## over the surfaces ##S_{1}, S_{2}, S_{3},...## below is a good way of finding the average of the volume integral of ##\textbf{B}## in the neighborhood of these surfaces. More specifically, he says in page...
  20. A

    Rotational Mechanics -- A solid sphere is rolled on a rough surface

    I found out the time when rotation ceases to be 4 ##v_0## /5*mew*g, where mew=coefficent of friction of surface but I am unable to plot the graph post that time
  21. F

    I The 'outer surface' should be redefined when applying Gauss' law?

    Gauss' law dictates that charge will only appear on the outer surface of a conductor. But if there's charge in a conducting cavity, the inner surface of the conductor will accumulate induced charge. So what's outer or inner should be redefined?
  22. B

    Max surface charge of a conductive plate

    1. Can I use the surface charge equation: $$Q = \frac{Vk\epsilon_0A}{d}$$ Where V = Voltage, k = dielectric constant, ϵ0 = permittivity of free space , A = Area of plate and d = distance between plates. For a conductive plate within an electric field? My thinking is that if the plate is...
  23. E

    A How to understand when surface terms go to zero

    Hi all, I'm trying to understand when surface terms go to zero. I'm not really getting a connection other than many textbooks just saying surface terms go to zero. I have added a photo of Liboff's Kinetic Theory page 3 on Lagrange's equations. Before equation 1.7, he says the surface terms go...
  24. Adesh

    I What is the meaning of the free surface in fluid mechanics?

    I’m currently studying Fluid Mechanics, during an analysis I came across this We now consider an example that combines centrifugal force and gravity: a liquid in a drum (centrifuge) rotates with constant angular velocity ##\omega## about a vertical axis. The centrifugal force per unit of...
  25. E

    Friction force of 2 connected block on steel surface

    hello there, I am wondering if my attempt at a solution for this particular problem correct?? I mean I know that the blocks won't move and the total friction force is 38.95N (at least lesser than that, since that is the maximum static friction). I saw someone attempted the solution but it is...
  26. Zohar

    B Why does coffee in a glass leaves its signatory on the surface?

    Some of us may use coffee coaster for our drinks. I was always wondering about that phenomenon and failed to find something on the net yet.
  27. Glenstr

    I Objects flying over the lunar surface

    This video has been popping up in my feeds over the last day or so, as I'm sure others here have also seen it by now. Looks like it has been taken with one of these super zoom cameras. After watching it carefully several times, it doesn't appear to be done with creative video editing, which I...
  28. Zohar

    Viscoty and Surface tension -- depends on the composition of the atmosphere?

    why isn't Surface tension reliant on the composion of the atm? For an instance; If you place a glass of water in a room with regular atmosphere or you place it in a room filled with other gasses. The coefficient of surface tension of the fluid will change? Maybe? why isn't viscoty of a fluid...
  29. T

    I Surface of a cone by integration

    If i want to calculate the volume of a cone i can integrate infinitesimal disks on the height h of the cone. I was told that if i want to calculate the surface of the cone, this approximation is not correct and i have to take the slanting into account, this means that instead of...
  30. C

    Potential vector (A) of a disk with a surface current

    Hi, I've been stuck for a long time with this exercise. I am not able to calculate the potential vector, since I do not know very well how to pose the itegral, or how to decompose the disk to facilitate the resolution of the problem. I know that because the potential vector must be parallel to...
  31. VVS2000

    Surface integrals to calculate the area of this figure

    I can find the area of the triangles but can't solve the squares for some reason
  32. F

    Arbitrariness of the surface involved in the displacement current

    I was thinking of a standard, high school level discussion of the displacement current. The need for introducing this quantity is demonstrated by considering a circuit with a charging capacitor, and (for the sake of simplicity) a circular loop whose axis is along the (straight) wire carrying the...
  33. Behrouz

    Surface temperature-laser radiation

    Hello, I'm looking for the governing equations for the laser radiation on a surface. I understand there are several types and methods. I was wondering if there is an equation to show all the parameters in calculating a surface temperature after laser radiation for a specific time. Some of the...
  34. Elder1994

    Verify Stokes' Theorem for this vector field on a surface

    I do not understand how can I parameterize the surface and area and line differentials.
  35. G

    B An intrinsic equation of a surface

    Is there an equation that a surface dweller could developedto globally describe his or her surface? Let us say a sphere? If we determine that curvature is everywhere constant what would be an equation that would describe that surface ? (simply that curvature is everywhere constant?) And if...
  36. K

    Static friction — Experiment pulling different blocks across a surface

    I know that I am supposed to use the equation I wrote, but how do I find the maximum force of static friction and coeffcient of static friction if none of them are given beforehand? I can't have to unknowns in an equation. We then did the same thing, the only difference was then to measure the...
  37. S

    Potential difference between the surface of a sphere and a point far away

    V at surface = k Q / r = 9 x 109 x (1 x 109 x (-1.6 x 10-19) / (1 x 10-2) = - 144 V V at a point far away = 0 V From the sentence "electric potential difference between the surface of this sphere and a point far away" means that the question asks about V at surface minus V at far away so the...
  38. D

    Flux of a vector field through a surface

    Given ##F (x, y, z) = (0, z, y)## and the surface ## \Sigma = (x,y,z)∈R^3 : x=2 y^2 z^2, 0≤y≤2, 0≤z≤1## i have parametrised as follows ##\begin{cases} x=2u^2v^2\\ y=u\\ z=v\\ \end{cases}## now I find the normal vector in the following way ##\begin{vmatrix} i & j & k \\ \frac {\partial x}...
  39. A

    Resources on non-spherical conductor surface charges

    Hi all, I know qualitatively that charges tend to concentrate on sharp edges of conducting surfaces. I have tried searching online for a mathematical treatment of such a phenomenon, but I cannot find anything that's quite rigorous. I'd appreciate it if someone could guide me towards such...
  40. lomidrevo

    B The highest resolution image of the Sun’s surface ever taken

    Full article: https://www.aura-astronomy.org/news/nsfs-newest-solar-telescope-produces-first-images/
  41. chriscarson

    Finding the the area of the surface at one end of the steel

    Is there any mistake in the following answer because I m always getting the result of 10362 mm 2 ? A piece of steel tube, has an external diameter of 140mm and an internal diameter of 80mm. What is the area of the surface at one end of the steel? Answer (13424 mm2)
  42. Kaushik

    Why does an increase in surface area lead to a reduction in pressure?

    From what I read on the internet I found that increase in surface area that is in contact is offset by the reduction in pressure. What exactly does it mean? This is what I understood from the it (but my understanding might be absurd :-p): does reduction in pressure mean that the "hills" or...
  43. R

    Collision between a block and a curved up-ramp surface

    I tried to solve this question using conservation of momentum. The momentum of the system is mc(vc)=mcvc'+mbvf'. But after that I have no idea I want to use the conservation of kinetic energy but the question doesn't say it's elastic collision, I need to find the velocity of the mb after the...
  44. K

    A Differential movement along a curved surface

    I'd like to understand the movement of a particle along the surface of a three dimensional graph. For example, if there is a flat two dimensional plane (z=2 for all x and y), and a unit vector describes its initial direction of movement (<sqrt(2)/2i+sqrt(2)/2j> for example), then the vector...
  45. omega_minus

    Surface speed of a strip over a deflection roll

    Hello, I am trying to solve a problem at work that at first I thought was easy but has proven trickier than I originally thought: If I have a strip of material traveling in a straight line and it is tangent to a roll turning below it, the roll would need to turn at the surface speed of the...
  46. bravopipo

    Maximum load capacity of a time dependant Force on the surface of a metal

    Hello; What equations on mechanics can I use or study in order to measure the maximum force in Newtons the surface of the metal Steel box can hold. Details: Watch the image below, we have a metal box made of let's say steel, this box have a shape of rectangle of a thickness of for example 1cm...
  47. Vivek98phyboy

    Force due to Surface tension here

    Why does the force due to surface tension act parallel to the surface here? I know that surface tension is a result of absence of cohesive force above the surface and thus the water molecules below pulls the surface down and keeps it like a stretched membrane. If the surface is pressed as...
  48. Z

    Find the electric field on the surface of a sphere using Coulomb's law

    Note that the solution is 5625 V/m in z direction which is found easier using Gauss' law, but I want to find the same result using Coulombs law for confirmation. Lets give the radius 0.04 the variable a = 0.04m. ##\rho## is the charge distribution distributed evenly on the surface of the...
  49. C

    Surface Charges on a Coaxial Cable

    To find ##\sigma_b## I can use a Gaussian surface of a cylinder of length ##L## and radius ##c>r>b##. Since that is inside of the outer conductor, I know the electric field is zero, so I have from Gauss' Law, $$0=2 \pi L\left(b\sigma_b+a\sigma\right)$$ and easily solve for ##\sigma_b##. For...
  50. Vivek98phyboy

    Reason for Calculating Surface tension

    When calculating force due to surface tension across a hemispherical drop, we look at only the circumference and multiply it by the value of surface tension. When we know that it is the surface tension which is responsible for the curved surface of the liquid drop, why don't we calculate the...
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