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. AllenFaust

    Hamiltonian for a dimer approaching a surface

    Hi! it's been a day since I have started this problem. I was wondering how I could arrive to this Hamiltonian? And I'm a bit at a lost on how exactly to derive this? I hope anyone can help me with this, even a suggestion of good starting point would be much appreciated. Basically the problem...
  2. AdrianMachin

    Calculating work on an electron on an equipotential surface

    This is not a homework, but a question formed in my mind after reading my textbook. Homework Statement Consider an electron (a charged particle) on a metallic equipotential surface. We know that all the points on the surface are equipotential, thus there will be no force on charged particles...
  3. P

    Surface impedance in porous rigid materials

    Hi guys, I've got an exam in a few days and my lecturer is unresponsive, so wondering if you can help me. The question I am solving is the following: Calculate the impedance at the surface of a layer of spruce wood of thickness d equal to 2mm, and of density rho equal to 0.47 Mg/m3 at...
  4. S

    Motion on a frictionless Surface

    "Suppose a body is kept on frictionless surface (considering gravity is acting on a body). If we give a little push to the body, will it conitnue to be in state of motion with constant velocity or not?...If yes then why?? (Considering all resistances to be zero ..)
  5. P

    Friction between cart and a surface covered with a liquid?

    << Thread moved from the technical forums so no Homework Help Template is shown >> Hello, I'm attempting an experiment where I take a cart and slide it down a ramp. Each time, I will coat the ramp with a different liquid. I want to compare the effects of the dry ramp, a ramp with water poured...
  6. Y

    I How does divergence calculate all of flow through a surface?

    I'd like to use 2-d for simplification. Divergence is the rate of change of a component of a field F as you travel along that component's direction. So Fx represents the part of F flowing the X direction and same with Fy along the Y direction, and so divergence is calculated by dFx/dx +...
  7. Kevin Shen

    Pressure, surface area and force in tire

    Assuming that the temperature in the tire suddenly rises. My question is that would that cause the contact surface area between the tires and the floor increase, decrease, or stay the same? (given that the volume of air in the tires is a constant and cannot be changed) Also, why?
  8. R

    Is there any way to calculate this integral?

    I have done it by the parametric form of σ, but if I change σ to implicit form that is G(x,y,z)=x^2+y*2+z^2-R^2=0 I don't know how continue. The theory is: where Rxy is the projection of σ in plane xy so it's the circumference x^2+y^2=R^2
  9. V

    I Why does low surface energy imply hydrophobicity?

    I don't understand why materials with low surface energy are hydrophobic and viceversa. All I can find are quick phenomenological explanations that don't quite deal with the physical (microscopic) process going on. Could anyone provide a good microscopic picture of why it is that way? What's...
  10. T

    Rolling a spray paint cap on a surface

    Hi there, I noticed that when I release the cap it moves forward slightly (away from me) which I attribute to the surface being not level and my hand applying a small force. However, the cap will roll backwards afterwards (towards me). What is causing the cap to roll back and forth? It...
  11. Pushoam

    B Closed surface bounding a volume V

    Is a surface bounding a volume always a closed surface?
  12. I

    Finding distance traveled by rebound when measured for surface

    Homework Statement Ball falling from 1m above a slanted surface 5 degrees from horizontal. KE conserved Find distance traveled along slanted surface on its second rebound Homework Equations S=(1/2)(at^2) (V^2)=(u^2)-2as The Attempt at a Solution V before hitting =sqrt(2*9.81) =4.42...
  13. A

    Temperature on the outer surface of insulation

    This seems basic, but I'm stuck. Look at the attached picture. I'm trying to find the temperature on the outer surface of the insulation. Is it not possible because I do not know the rate of heat transfer? How do pipe designers know the required thickness of insulation needed to reduce to a...
  14. R

    Maximum angular velocity of disc skidding across surface

    Homework Statement coefficient of kinetic friction between the disk and the surface is 0.42 gravity = 10.6 m/s disk mass = 1.75x10^9 the skid marks are 1280m long, This is due to the fact that uneven friction had set the saucer in very slow rotation around its principal axis. By...
  15. S

    Calculation of Pressure in a Cylinder with an orifice on its surface

    I want to calculate the pressure profile inside a cylinder whose initial pressure is less than the outside pressure and has a orifice on its surface to flow air through it. Air is a considered as compressible ideal gas and mass flow rate across a orifice is assumed isentropic. Also the...
  16. GAURAV DADWAL

    Problem with light grazing along the liquid surface

    Let's suppose we have a cuboidal tank filled with liquid of density rho,such that Critical angle of medium is (Ic) now it's Clear that light rays from the medium that strike at proper critical angle will Graze along the surface Now if someone would be along the path of the rays receiving...
  17. Mr Davis 97

    How Do You Choose the Correct Polar Coordinates for Surface Integrals?

    Homework Statement Solve the surface integral ##\displaystyle \iint_S z^2 \, dS##, where ##S## is the part of the paraboloid ##x=y^2+z^2## given by ##0 \le x \le 1##. Homework EquationsThe Attempt at a Solution First, we make the parametrization ##x=u^2+v^2, \, y=u, \, z = v##, so let...
  18. W

    Thermal resistance without area

    I'm (self)studying the physics of heat transfer at the moment. My book gives a relationship between heat transfer rate and thermal resistance as ##\phi=\frac {A \Delta T} {R}##. My book is not in English, so hopefully that is not the cause of this misunderstanding. I double checked that heat...
  19. S

    A Defining the surface gravity of a black hole

    Consider the following two definitions of the surface gravity of a black hole (taken from page 23 of Thomas Hartman's lecture notes(http://www.hartmanhep.net/topics2015/) on Quantum Gravity): 1. The surface gravity is the acceleration due to gravity near the horizon (which goes to infinity)...
  20. M

    What is Pressure and surface tension in fluids

    Today I was speaking with a professor and he asked me, regarding fluids, what is pressure. I said force per unit area acting normal to a surface. He then asked what I meant by surface. I wasn't really sure how to respond. He also asked me what surface tension was. I said it is a force per unit...
  21. M

    MHB How Much Netting Does Rita Need to Cover a Rectangular Area?

    Rita wants to cover a roughly rectangular area with netting. The height is 9 feet (but one side is along a solid fence, so could be 4 feet), two sides are each 6 feet, and the other side is 5_1/2 feet. How much netting does she need? Netting comes as a rectangular or square piece. My Work:Let A...
  22. N

    How weight affects surface bending over time

    Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...
  23. Zaent

    I Mean and Gaussian curvature for a Gaussian 'hill' seem wrong

    I'm hoping someone can help check whether my final contour plots look plausible based on the surface. I haven't done too much differential geometry but I've needed to work with Gaussian/Mean curvature for a simple 3D gaussian surface. Here's an example: (A = 7, a=b=1/(3.5)^2) It's...
  24. U

    B Integrating to find surface area/volume of hemisphere

    To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...
  25. L

    I How does Aluminum conduct electricity despite its non-conductive oxide layer?

    Aluminum metal covers itself immediately of an oxide layer in air. This layer is quite thick, more than 0,01mm they say and it's non-conductive. This layer infact is, e.g., thick enough to prevent soldering, further chemical attack by air oxygen or water (with which nude Al would immediately...
  26. DuckAmuck

    I Minimal Surface shape with gravity

    Minimal surfaces are sort of the "shortest path" but in terms of surface shapes. So I figured I could characterize the shape of a hammock by adding the influence of gravity, much like you can get the shape of a catenary cable (y=cosh(x)). The equation of motion I get from the Lagrangian is...
  27. Noaha

    Change in direction of electric field on conductor surface

    I would like to know why electric field of EM waves changes it's direction to opposite when hitting a conductor surface. I know that electric field inside a conductor is zero but I am not able to connect these two situations.
  28. itamar123

    Why are the traction vectors on each surface independent?

    Hey y'all, my first thread here, Got a burning question that has been disturbing my serenity. In all derivations of the stress tensor that I've seen they didn't explain it that much, So my question is, why do the traction vectors on each surface are independent? From what I understood, the...
  29. P

    Torque needed to start rolling motion on a inclined surface

    Hi, I need to choose a hydraulic hub motor for a vehicle which weighs 25 000 N when fully loaded. The vehicle must be able to start moving (fully loaded) on a inclined surface (30 degrees angle). So I need to determine the torque needed to get vehicle moving. The vehicle has three wheels from...
  30. B

    Electric field and surface charge density problem

    Homework Statement Homework EquationsThe Attempt at a Solution I don't understand how it looks like, how to approach this problem. I think it's maybe image charge or Laplace equation
  31. K

    How I can determine the free surface level?

    Hello My geometry is a prototype of a hydroelectric plant. It consists of a tank, penstock, a gate and a test section; my aim is to simulate turbulent flows on this prototype. My geometry consists of two zones, a zone filled with water (red color) and a zone filled with air (blue color). The...
  32. T

    Proving Normality to a Level Surface: A Derivation Approach

    Homework Statement Hi guys I am a bit stuck on how I am suppose to show, that thse funcitons are normal to level surface. I am I suppose to do a derivation of some sort, alls my notes say in a tiny box, that grad f is always in the direction to the normal of the surface. Do I have to calculate...
  33. Prateeksha Sharma

    How to design surface roughness model using CST?

    I am working om multilayer hybrid plasmonic waveguide (Si-SiO2-Ag_SiO2-Si). I have to see effect of roughness on propagation length and other parameters. So in reference to that I am having some doubts: 1) I use CST microwave studio for numerical simulation. I am not getting any direct option...
  34. alan

    Range in solid surface for liquid-liquid phase separation

    I am investigating the nucleation on solid surface during liquid-liquid phase separation, I know the free energy change is and I don't know if it is correct to get Can someone calculate it to have a check?
  35. Steven Hansel

    Why does the gravitational force decrease below the Earth's surface?

    Homework Statement Why does gravity force decreases below Earth's surface? Homework Equations F = G (m1 m2)/r^2 F = force of gravity G = Universal gravity constant m1 and m2 = mass of the objects r = distance between two objects g = GM/r^2 g = gravity of the object G = universal gravity...
  36. henry wang

    How does the surface property affect blackbody radiation?

    In an attempt to explain why a matt surface of aluminium is a better emitter/absorber of blackbody radiation than shiny surface of aluminium, my university lecturer suggested to me that: By brushing a metal surface to create a matt finish, the surface of the metal becomes rougher. Rougher means...
  37. P

    MCNP Error: JCO, Cell Cards & Surface Cards

    hi everyone, i have a mcnp error, it don't finish, it only run a half! i hope someone can help me! thank you! and my code JCO c cell cards 1 1 -0.00117 -100 300 2 2 -1.52 (-100:-101) -300 #1 $solution 3 4 -7.93 (-110:-111)#1#2 $clad 4 3 -1 (-200:-201)#3#1#2 $water 5 4 -7.93...
  38. Mind----Blown

    Surface current density-logic and definition contradict

    Okay, so in Griffith's introduction to electrodynamics, Griffith clearly defines surface current density as follows: "when charge flows over a surface, we describe it by the surface current density, K. Consider a 'ribbon' of infinitesimal width dL running parallel to the current flow. If the...
  39. D

    Electric potential of a conical surface

    Homework Statement (From Griffiths problem 2.26) : A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, and the radius of the top is R. Find the potential difference between points a (the vertex) and b (the center of the top).Homework...
  40. W

    Friction on a flat rotating surface

    If I push an object such as a cylinder of wood along a flat table (flat face of cylinder in contact with the table) through it's center of mass, the friction or energy required is not dependent of the surface area the block makes with the table, Friction = μ N, correct? And the energy required =...
  41. physicsdude101

    A mass is free to move on a horizontal frictionless surface

    Homework Statement A mass m that is free to move on a horizontal frictionless surface, is attached to one end of a massless string that wraps partially around a frictionless vertical pole of radius r, as in the Figure below.You are holding onto the other end. At t=0 the mass has speed V0 in the...
  42. Mictlantecuhtli

    Expressing surface charge density as volume charge density

    I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is...
  43. T

    B Existence of depletion layer in contact surface

    in a P-N junction diode, in an equilibrium state, a depletion layer forms in the surface of contact of N type and P type. But the problem is, this layer is formed by diffusion of electron to a lower electron density zone. Why does it always have to form right in the contactt surface? when...
  44. A

    I How come surface integrals are single integrals in my book?

    I am currently reading Young & Freedmans textbook on physics as part of a university course, and I've noticed that they repeatedly represent surface integrals (which are double integrals) as single integrals. For instance, they symbolically represent the magnetic flux through a surface as: \int...
  45. Cocoleia

    Electric field, surface charge density

    Homework Statement Homework EquationsThe Attempt at a Solution I have the full solution, the first part being: I don't understand how they came up with the expression for Vab. I know usually ΔV=-∫E dl, but I'm not sure how they found their expression. Can someone explain? Thanks.
  46. L

    Does entropy increase behind surface tension?

    Is there any entropic gain when the surface of a liquid is minimised? Per example, molecules "enjoy" maximum entropy when they are at the interior. Is this valid?
  47. M

    Calculate total energy surface tension

    Homework Statement Consider a planar liquid-gas interface and a solid sphere partially immersed in liquid. A fraction of the solid surface area is wet by the liquid, call it ##A_{sl}##. The complement of the solid’s area is ‘wet’ by the gas, say ##A_{sg}##. There is also an area of contact...
  48. A

    Do the radius of capillary affect the value of surface tension ?

    While going through the derivation to find the surface tension of liquid i came with the formula which says that the surface tension is directly proportional to radius of the capillary so does that imply if we use a capillary with a greater radius so the same will give the different value of...
  49. S

    Induced surface charge density

    Homework Statement Calculate the surface charge density induced by a point source above an infinite conducting plane, with 0 potential. Homework Equations ##E=-\nabla V## ##V=\frac{q}{4\pi \epsilon_0 r}## The Attempt at a Solution I used the method of image charges and I calculated the...
  50. T

    B About the surface area of a prolate ellipsoid

    Is there any limit for which we can approximately write the surface area of a prolate ellipsoid to be 4piA*B comparing with the spherical 4piR*R??
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