What is Surface: Definition and 1000 Discussions

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. A

    What is the relationship between surface tension and forces?

    Hello! To this I did what was recommended and this is what it looks like $$ F = mg $$ $$ F = \rho * V * g $$ $$ F = \ rho * \pi^2 * h * g $$ Than for the surface tension I did the same thing to get an expression for F. $$ y = \frac {F} {2 \pi r}$$ Than tried to get F out and than...
  2. J

    Typical surface roughness heights for aircraft surfaces

    Hello! I am investigating some preliminary aerodynamics on a regional turboprop and for the drag model the surface roughness height of the airplane is required as an input. For this i do not have any data. In which range are the typical values for modern aircraft surfaces? Thanks a lot!
  3. Martian2020

    B Why is air more dense closer to the Earth's surface? - particle's view

    Could not find reason on molecular level. E.g. here some explanation "There are two reasons: at higher altitudes, there is less air pushing down from above, and gravity is weaker farther from Earth's center." However, when I start to imagine particles, when there are only a few I get opposite...
  4. S

    Force at the end of a Rod at rest on an inclined surface

    Question diagram, attempt at solution below I need to cancel some of the terms in the moment equation but a not sure which ones to start with. I don’t know μ so can not calculate FA, so should probably substitute FA = RB2.
  5. Omega0

    B Inverse Transformation from Response Surface

    Let us say we have data which is for simplicity in N tables. All the tables have the same number of rows and columns. The columns ##A_i## have for all tables the same meaning (say measured quantaties like pressure, temperature) where the first 3 columns is the position in space. Again for...
  6. EnergyInMotion

    Reflection of Radio Waves by a Mirror-like surface

    Hey guys, I'm new to the physicsforums. I wanted to share some videos I made and see if anyone was interested or wanted to discuss what they see. In this video I show in a manner in which is VERY easy to see, that a reflective surface will reflect not just light but also radio waves (and most...
  7. S

    Can a diamond's color be simulated by only a surface coloring?

    I was reading this article about the a replica of the famous Hope Diamond and its antecedents: https://www.nytimes.com/2020/11/28/style/hope-diamond-story-smithsonian-copy.html This part seems to say that the color is to be simulated by a coating: It would seem to me that the proper attenuation...
  8. L

    Magnetic Flux through a Closed Surface and Maxwell's laws

    Hi everyone, I have a question about Maxwell's laws. According to Maxwell the magnetic flux of a magnetic field through a close surface is 0. But his third law says the circuitation of an electric field depends from magnetic flux variation. I can't understand how this can be possible since...
  9. Adams2020

    I The surface area of an oblate ellipsoid

    In "An Introduction to Nuclear Physics by W. N. Cottingham, D. A. Greenwood" for the surface area of an oblate ellipsoid, the following equation is written for small values of ε : The book has said this without proof. I found the following formula for the desired shape: No matter how hard I...
  10. Monoxdifly

    MHB [ASK] Minimum Surface Area

    The volume of a cuboid box with a square base is 2 litres. The production cost per unit of its top and its bottom is twice the production cost per unit of its lateral sides. Suppose the side length of its base is x and the height of the cuboid is h. The minimum production cost is reached when...
  11. N

    Motion inside a curved surface

    Here's my solution: I've tried to find the equation of vx. But the graph that it is generating is not right. I am not able to figure out what is wrong in the equation for vx. Please let me know where is the equation wrong and what is wrong? Here's the graph:
  12. D

    Lens selection for close proximity surface photos

    Good day all, I am searching for some advice on how I could successfully take photos of a surface that is 5mm away from a CMOS camera sensor. My ideas so far are; 1.) Find a lens with sub millimeter focal length (0.2mm by my calculations) 2.) Utilize mirrors to increase object distance 3.) Pin...
  13. TheGreatDeadOne

    Using the Divergence Theorem on the surface of a sphere

    The integral that I have to solve is as follows: \oint_{s} \frac{1}{|r-r'|}da', \quad\text{ integrating with respect to r '}, integrating with respect to r' Then I apply the divergence theorem, resulting in: \iiint \limits _{v} \nabla \cdot \frac{1}{|r-r'|}dv' =...
  14. A

    Analytical Mechanics: Regularity Conditions on Constraint Surface

    Hi, In my course in analytical mechanics, it is said that for a system of n particles subjected to r constraint equations, it is necessary to impose regularity conditions on the constraint surface defined by G = 0 where G is a function of the position of the position of the particles and time...
  15. A

    Vertical beam on a frictionless surface

    This could also be posted in the Math / differential equations sub, but it also involves the derivation which is classical physics. So I was doubting :smile:. So, I'm dusting off my dynamics a bit and found this problem of a thin beam on a frictionless surface in a different forum and decided...
  16. WhiteWolf98

    Surface Pressure Coefficient Distribution of a Doublet in a Uniform Flow

    So, it's a long way to the solution, but I'm finding it difficult to find a starting point. I'm going to say that as a first step, I should find what the value of the stream function ##\psi## is, at the surface. In order to do this, I need to use the following equation: ##F=\phi+i\psi## If I...
  17. andyonassis

    Finding the angle between a plumb line and the Earth's surface.

    From Newton's second law: $$T_{x} = F_{turn}$$ So $$T \sin \theta = ma$$ $$T_{y} = F_{y}$$ so $$T \cos \theta = mg$$ Equate the two equations to get: $$ \frac{T \sin \theta}{a} = \frac{T \cos \alpha}{g} $$ and the angle is given by: $$tan (\theta) = \frac{a}{g} $$ where ##r = \frac{v}{w}## and...
  18. Mr_Allod

    Bound Bulk Current Density and Surface Current Density

    Hi there, I've worked through most of this question but I'm stuck on the final part, showing that total bulk current ##I_B## is equal and opposite to total surface current ##I_S##. I calculated ##\vec H## the normal way I would if I was looking for ##\vec B## in an infinitely long cylindrical...
  19. F

    Water flow rate and drip surface tension

    hello i have a drip tube with water dripping and when i increase the flow rate or frequency of drips they get bigger/more massive. i see the equation mass x gravity = 3.14(tube diameter)(surface tension) my mass is changing but not gravity, 3.14 or tube diameter so surface tension must be...
  20. Hamiltonian

    B Doubt on the derivation of an equation for a surface integral

    this method of derivation is approximating the function using a polyhedron. concentrating on one of the surfaces(say the L'th surface which has an area ##\Delta S_l## and let ##(x_l,y_l,z_l)## be the coordinate of the point at which the face is tangent to the surface and let ##\hat n## be the...
  21. K

    Surface integral: Calculate the heat flow from a cylinder

    Hi, I am trying to calculate the heat flow across the boundary of a solid cylinder. The cylinder is described by x^2 + y^2 ≤ 1, 1 ≤ z ≤ 4. The temperature at point (x,y,z) in a region containing the cylinder is T(x,y,z) = (x^2 + y^2)z. The thermal conductivity of the cylinder is 55. The...
  22. rbmartel

    I Which area should I use to calculate the force on a submerged surface?

    Let's say we have a tank filled with water only half way up. I want to calculate the force being applied by the liquid on one of the walls, that's F = P.A. For the area (A), should I consider the area of the entire wall (H.L), or only the area of the wall that's in contact with the liquid...
  23. S

    Strange pattern on a concrete paved surface

    I found this funny pattern in a slightly damp concrete paved parking area. Any ideas what it is?Detail :
  24. CatalinaAlmendra

    Chemistry How Does Surface Area Affect the Free Energy of a Liquid?

    Hello, so first of all I want to clarify that english is not my first lenguage, so I'm really sorry for possible future errors. Second, this is a problem from my physical chemistry class, and I'm not sure where it fits better, if here or in the physics homework help, I'm sorry :( So, I don't...
  25. M

    Divergence Theorem Verification: Surface Integral

    Hi, I just had a quick question about a step in the method of calculating the surface integral and why it is valid. I have already done the divergence step and it yields the correct result. Method: Let us calculate the normal: ## \nabla (z + x^2 + y^2 - 3) = (2x, 2y, 1) ##. Just to double...
  26. archaic

    Maximum electric field at the surface of a Van de Graaff generator

    I know that the potential of the sphere at its surface is ##V(a)=kQ/a##, and the electric field generated by it is ##E(a)=kQ/a^2##, which gives me ##V(a)=aE(a)##. When the electric field at the surface is as in the question, we have...
  27. archaic

    Finding net charge on a sphere's surface

    The electric field caused by the surface distribution on a point ##a## meters far from it is$$E(a)=\frac{kQ}{(R+a)^2}$$from which I get$$Q=\frac{(R+a)^2E(a)}{k}=\frac{(R)^2E(0)}{k}=\frac{(0.705)^2\times867}{8.99\times10^9}\approx4.79\times10^{-8}$$and I take its negative because the direction of...
  28. agnimusayoti

    Electric field a distance z from the center of a spherical surface

    Well, I really don't understand what is the use of the hint. I try to solve this problem with Coulomb's Law and try to do in spherical coordinates and got very messy infinitesimal field due to the charge of infinitesimal surface element of the sphere. Here what I got: $$\vec{r}=\vec{r_P} +...
  29. Isaac0427

    I Confirming my knowledge on surface integrals

    Hi, I want to make sure my understanding of calculating surface integrals of vector fields is accurate. It was never presented this way in a textbook, but I put this together from pieces of knowledge. To my understanding, surface integrals can be calculated in four different ways (depending on...
  30. M

    How is this formula for the surface derived?

    The pages shown in the pictures are from an engineering book. I am not sure how the thickness of sphere plays a role in the inner surface of the sphere. I know that the surface area of sphere is ##4 \pi r^2 ## . Picture 2 shows how that formula plays a role in understanding the stress...
  31. A

    Problem in the parametrisation of a surface

    Good day my question is the following: How did they determine the the orientation of the first and last loop? and why in the parametrisation of the second loop we have: (3cost;-3 sint;1/2) ( the negative sign puzzles me) thanks this is the solution of the book
  32. A

    Problem figuring out the surface of integration

    Good day I have a problem figuring out the surface of integration according to the exercice, we have a paraboloid that cross a disk on the xz plane, the parabloid cross the xz plane on a smaller disk r=√3/3 so for me after going to the final step of integration and using polar coordinate i...
  33. U

    I Fixing an orientation for a connected smooth surface

    I am studying on Zorich, Mathematical Analysis II, 1st ed. pag. 174-175. After having properly explained how orientations (equivalence classes) are defined for smooth k-dimensional surfaces in ##\mathbb {R} ^ n## that can be described with a single map, move on to the more general case by...
  34. Tony Hau

    What is the meaning of electric field "immediately outside the surface"?

    Today when I am reading Griffith's electrodymamics on surface charge and force on conductors, I have come across two very ambiguous terms: electric field at the surface and immediately outside the surface. The context of these two words is as follows: The electric field immediately outside is...
  35. U

    I Calculating Surface Area of Schwarzschild Black Hole w/Weyl Coordinates

    Recently, I was tasked to find the surface area of the Schwarzschild Black Hole. I have managed to do so using spherical and prolate spheroidal coordinates. However, my lecturer insists on only using Weyl canonical coordinates to directly calculate the surface area. The apparent problem arises...
  36. brotherbobby

    Surface Tension - Using hot soapy water to wash clothes

    I mention the details in the book (verbatim) in the form of a paragraph in green below. Later I ask my questions in blue font for better reading. "Surface tension also explains why hot, soapy water is used for washing. To wash clothing thoroughly, water must be forced through the tiny spaces...
  37. S

    A How does the number of particles increase the surface adsorption?

    How the number of the particles in a solution increase the probability to get adsorption on a surface? which physical terms explain this? For example when I increase the concentration of molecules in a solution I can see that the adsorption and the aggregation on the surface happen.
  38. M

    A Clarifying question about surface states

    Recently, I was giving a presentation for my research group related to ARPES to improve my understanding. I mentioned that the probing depth of ARPES is a few angstroms, meaning we can only look at surface states, and I was sort of giving a real space picture. In other words, ARPES can only...
  39. 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
  40. A

    Rough surface of swift wings

    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...
  41. 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
  42. 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
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  49. 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?
  50. 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...
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