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. G

    MHB What is the area of Angular Land below sea level?

    The area of ​​Angular Land is described by inequalities | x + 5y − 28 | ≤30 and | 3x + 5y −34 | ≤30, where the point with coordinates (x, y) is the point distant x kilometers east of a certain reference point (in the case of x negative, this is a point | x | kilometers west) and y kilometers...
  2. Wi_N

    Calculating the surface area of a solid of rotation

    For some reason I have become very unsure but my gut feeling says i can calculate y=(1-x^(a/b))^(d/c) I already know the formula for calculating the volume. but can transfer the whole thing as a function of y(x) and take the integral then as a single integral?
  3. P

    Finding the flux along the curved part of a surface

    I have this problems I am trying to figure out: So I know that $$\int B\, dA = 0 = \phi_{total}$$ $$\phi_{total} = \phi_{bottom} + \phi_{top} + \phi_{side} = 0$$ $\phi_{side}$ must be equal to the other two fluxes, since they are both outwards: $$\phi_{side} = \phi_{bottom} + \phi_{top}$$...
  4. torito_verdejo

    I Gauss' Law applicability on any closed surface

    I have read multiple threads on Physics Forums, Stackexchange and Quora, as well as the explanation of Gauss Law, but still don't understand the most fundamental aspect of it: its applicability for any kind of surface. More precisely, I don't get how this follows from the fact that...
  5. L

    MHB Compute probability closeness between points in a 2D surface

    Hi all, Sorry, in my first message, I posted this question in the Basic Probability section, and so I moved it to this section. I have a surface (for example, a blank paper). In this surface, I have some elements of the set "A" randomly distributed. In this surface, I also have some elements...
  6. Y

    Misc. How to thin out the back without making any scratches on the surface (earrings)

    Hi I want to modify a pair of Halloween earrings for my wife, it's a pair of pumpkin earrings, the problem is the other side is just flat black, only showing the pumpkin on one side. I want to get two pairs and glue them back to back so I get pumpkin on both sides. The problem is it's going to...
  7. Frigus

    Surface Tension: Why Tangential and Not Downward?

    Why direction of surface tension is tangential to the surface and not perpendicular downwards since it is caused by molecules in the bulk?
  8. Frigus

    Classical Resnick Halliday Walker -- do they discuss surface tension topic?

    Is surface tension topic present is resnick halliday walker, principles of physics 10th edition,if present then please tell me on which page
  9. Clay Gillespie

    B Angular Meteorite Strikes on the Moons Surface

    Summary: An explanation into the mechanisms that make irregular shaped meteorites, including some up one tenth the size of the moon, seemingly vanish, leaving symmetrical craters with surprisingly shallow floors. We’re going to look at the initial conditions of the moons formation from the...
  10. S

    I Strain of of a bubble's surface interface during vibrations

    Imagine a bubble vibrating in air. Because it vibrates, it's interfacial area increases, thus new molecules are added and removed from the surface as it vibrates. Consider a molecule is initially at position X_0 at the interface, and over a certain amount of time molecules squeeze and disappear...
  11. S

    I Proving Gauss' Law using a Cubical Surface

    Hi, I'm trying to prove Gauss's Law by using a cubical surface with a point charge located at its center, and I'm running up against some difficult integration. I've worked through the first integral of the surface integral, but I can't seem to figure out a proper integration technique. Here is...
  12. Beelzedad

    I Swapping the order of surface and volume integrals

  13. B

    How does the surface of a refracting prism become reflective?

    In my physics lab, we placed a mirror in front of a telescope with built in crosshairs and crosshairs that were shining out the front of the telescope which reflected against the mirror and allowed us to see them and then adjust the level of the telescope until the two were aligned. Later we had...
  14. B

    How does the surface of a refracting prism become reflective?

    Homework Statement: How does the surface of a refracting prism become reflective? Homework Equations: None In my physics lab, we placed a mirror in front of a telescope with built in crosshairs and crosshairs that were shining out the front of the telescope which reflected against the mirror...
  15. Beelzedad

    I Is interchanging the order of the surface and volume integrals valid here?

    Consider a continuous charge distribution in volume ##V'##. Draw a closed surface ##S## inside the volume ##V'##. Consider the following multiple integral: ##\displaystyle A=\iiint_{V'} \left[ \iint_S \dfrac{\cos(\hat{R},\hat{n})}{R^2} dS \right] \rho'\ dV' =4 \pi\ m_s## where...
  16. Samanko

    Surface charge density of a conducting spherical shell

    The textbook says ' A conducting sphere shell with radius R is charged until the magnitude of the electric field just outside its surface is E. Then the surface charge density is σ = ϵ0 * E. ' The textbook does show why. Can anybody explain for me?
  17. Like Tony Stark

    Vehicle moving along a path tangent to the Earth surface

    Here I have some problems. I get confused when it says"with respect to the path", is it different from "with respect to the earth"? Because the path is on the Earth. Then, the vehicle is not accelerated in the vertical direction because it moves along the path, is it?
  18. A

    Earth-like planet with 2x surface area, but same surface gravity?

    How feasible is such a planet? Can the planet still be dense enough to be rocky and not gaseous?
  19. E

    Venera 13 photos from the surface of Venus

    In 1982, the USSR sent a space probe named Venera 13 to land on the planet Venus. The lander lasted only two hours before succumbing to the extreme temperatures and crushing pressures on the surface of Venus, but not before it sent back these stunning photographs.
  20. patricio ramos

    Engineering Pressure Force on a partially submerged surface

    Once I get the pressure, do I have to multiply times de area that is submerged (in this case it would be 25m^2), or do I take the whole area of the plate, including the part that is not submerged (in this case it would be 30 m^2) Thanks
  21. cynth

    A Fermi surface and electronic correlations

    why an increase of fermi pockets leads to a reduction of electronic correlations
  22. F

    Which force is responsible for light's reflection in a surface?

    I think I understand how electromagnetic force works, so I predict that if I take a big, big, long flat table, charge that table with a big negative electric voltage (say -500kV), then I shoot an electron at that table at an angle, then the electron will be repulsed by the charge, will make a...
  23. Adesh

    How to find the volume under a surface?

    I want to know that how can z=$$ \sqrt{1-x^2}$$ ever represent a surface? It graphs a curve in the x-z plane and the triangle lies in x-y plane so how can they contain a volume, they are orthogonal to each other. I have attached awn image which is drawn GeoGebra for the function...
  24. wirefree

    Does Surface Thickness Affect Flux Calculations?

    I greatly appreciate this opportunity to submit a question. Is the thickness of a surface of any relevance while estimating the flux through it, as is mentioned in the following? Thankful for any advice.wirefree
  25. P

    I Circumference of a circle on a spherical surface

    I was just reading an intro text about GR, which considers the circumference of a circle on a sphere of radius R as an example of intrinsic curvature - the thought being that you know you're on a 2D curved surface because the circle's circumference will be less than ##2\pi r##. They draw a...
  26. T

    Surface smoothness of a slowly frozen metal droplet

    Would a small (of order 5 microns to 0.5 mm) liquid metal droplet, if cooled slowly away from external perturbations and not in the presence of oxygen, retain its highly smooth and polished surface as it froze? What phenomena would influence the surface roughness? I assume that simple density...
  27. A

    Newton's Laws — Pushing a box horizontally on a surface

    unsure what process to tackle it.
  28. K

    Scratched Surfaces: Chemistry & Health Impacts

    When something in our daily life used for years we could often find its surface scratched slightly, even if we use it very carefully and don't make scratches intentionally. I'd like to know, from chemistry or molecular point of view, did it lose any atoms or particles away from the scratched...
  29. X

    MCNP error surface 0 not found for cell 101

    Hello, I am working through the MCNP manual and am experiencing the following error as well as warning when trying to run the sample problem from the manual. The fatal error I get is "fatal error. surface 0 not found for cell 1050." I have upload the output file with the errors in case I...
  30. T

    A Identifying a surface as a cone

    Hi, I’m using some CAD software trying to automate some surface identification, and I’m looking to find a way to identify whether a surface is a cone. I will have access to vertices and normals at discrete points on the surface, but it will be expected that the number of these points will be...
  31. G

    On the motion of a particle on the inner surface of a sphere

    Could anyone please help me out with the second part of this question: I've got the first part, u = √(5ga) Here's my diagram for the second part: Distance traveled is from bottom of sphere to peg is 2πa/3 which means angle traveled is 2π/3. So the particlee is going to travel 2π/3 radians...
  32. CRuff

    Detectable wavelengths of light at the surface of the Earth

    I am sure this will become a 'face-palm' moment, but can anyone point me in the direction of what electromagnetic energy wavelengths on either side of the visible spectrum, that is detectable on earth, ie what is not filtered by our atmosphere? I am specifically trying to find information on the...
  33. T

    Tensile Test Results: Adhesion of Tape to Plastic Surface

    Hello, I am currently writing my thesis, where I have to investigate if a surface treatment increases the adhesion (between tape and a plastic surface). For this purpose, I have among other tests, performed a tensile test between the tape and plastic surface. The tensile test can be separated...
  34. M

    Solar pool heating via a dark screen -- On the surface or submerged?

    Summary: Looking for input on either floating or sinking a large sheet of dark screen for solar absorption in a pool Looking for input on either floating or sinking a large sheet of dark screen for solar heat absorption in a pool. My though its that screen would be very user friendly to roll...
  35. J

    Work done by varying friction against a constantly moving surface

    Suppose a metal disk is spinning at constant rate of one cycle per second and at a radius of about four inches a small metal block is pressed against the disk. The circumference of the path of the contact is exactly one foot. The coefficient of kinetic friction between the disk and the small...
  36. E

    MHB Surface Area of Revolution with Double Integration

    Please Help Me
  37. charlesmartin14

    How to compute the surface an N-sphere using delta functions

    Problem Statement: I am trying to understand how to compute the surface an N-sphere , for large N, to leading order (and exactly) Given a vector J with norm N, with N large, how does one compute the volume integral ? That is, what representation of the delta function. And what is the exact...
  38. A

    Is this surface integral correct?

    Problem Statement: Requesting for re check Relevant Equations: Requesting for re check In this eq.A4 putting ##v=Hr+u## the first integrand in eq.A5 is coming as ##H(r(\nabla•u)-(r•\nabla)u+2u)\ne\nabla×(r×u)## Am I right?? Can I request anyone to please recheck it... using this the author...
  39. A

    Normal Velocity Gradient Across a Surface: Proving a Result

    I have came across a problem where each point of a surface parallel to the x-y cartesian plane and having it's normal along the z axis is having velocity along the z direction ##v_z## and there exists a velocity gradient across the plane (e.g ##v_z(x,y)## , After time ##\delta t## it is written...
  40. fluidistic

    A What can the Fermi surface tell us about a material's properties?

    I would like to know every bit of information one can retrieve by looking at the Fermi surface of a material. Here's what I think is correct thus far: 1) The fact that the material has a Fermi surface already tells us a lot. The material could be a metal or something that resembles a metal...
  41. alexmahone

    Average electric field over a spherical surface

    I'm sure the average is going to be an integral, but \displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a} gives me a scalar, not a vector.
  42. A

    How to solve a surface double integral?

    Hi I´d like a suggestion about a surface double integral. If I have a sphere x^2+y^2+z^2=4 is on the top of a cardioid r=1-cosθ. The problem is when I solve the integral I got a inverse sine when the answer is a natural logarithm (ln)
  43. maistral

    I Fitting points z = f(x,y) to a quadratic surface

    Hi! I am aware that standard fitting numerical methods like Levenberg-Marquardt, Gauss-Newton, among others, are able to fit a dataset z = f(x,y) to a quadratic surface of the form z = Ax2 + Bxy + Cy2 + Dx + Ey + F, where A to F are the coefficients. Is there a simpler method that exists? I'm...
  44. E

    Show that a tilted free liquid surface undergoes shear stress

    i really can't understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow. i...
  45. DavidMasabo

    Need a force to accelerate an object on a frictionless surface

    Problem Statement: would you need a force to accelerate an object on a friction-less surface? How could one calculate the force? Relevant Equations: F=MA would you need a force to accelerate an object on a friction-less surface? How could one calculate the force?
  46. M

    Export a 3d surface movie with good quality

    Hi PF! I have a 3D surface that changes with time. I am trying to make a movie. The following is what I do, but the output is extremely low quality. Does anyone know how I can get the same quality that Mathematica uses for its images? mov[t_] := Show[ParametricPlot3D[{(2 + Cos[v]) Cos[U]...
  47. mishima

    Calculus of Variations, Isoperimetric, given surface area max volume

    My volume integral is... $$\pi\int y^2 dx$$ My surface area integral is... $$2\pi\int y \sqrt {1+x'^2} dy$$I'm fairly sure the variable of integration on my volume and surface area integrals has to be the same, is that right? But when I change the variable in the surface area integral to...
  48. M

    I Showing that B has no discontinuities at the surface

    Consider a magnetic dipole distribution in space having magnetization ##\mathbf{M}##. The potential at any point is given by: ##\displaystyle\psi=\dfrac{\mu_0}{4 \pi} \int_{V'} \dfrac{ \rho}{|\mathbf{r}-\mathbf{r'}|} dV' + \dfrac{\mu_0}{4 \pi} \oint_{S'}...
  49. M

    What will the electric field be at the surface?

    The electric field due to a dipole distribution in volume ##V'## can be viewed as electric field due to a volume charge distribution in ##V'## plus electric field due to a surface charge distribution in boundary of ##V'##. ##\displaystyle\mathbf{E}=\int_{V'} \dfrac{\rho...
  50. M

    Prove the dipole potential is differentiable everywhere except at the surface

    The dipole potential is given by: ##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV' +\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'## I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous) I know if...
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