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. T

    Measuring surface waves using the a pressure sensor?

    Not sure if this is an engineering or physics question, but here it goes: I'm trying to wrap my head around the pressure field caused by waves. I'll recap to so anyone can check if I have made any incorrect assumptions: If we ignore atmospheric pressure, the pressure in the water has a...
  2. I

    Quickie: vector normal to surface

    Homework Statement Find vector normal to z = x^2 + y^2 - 3 at point r = (2, -1, 2) Homework EquationsThe Attempt at a Solution here is the markscheme. I understand how to find the gradient, but i don't understand how they calculated the magnitude. thanks
  3. B

    Find the magnetic field of an infinite uniform surface

    Homework Statement This example is from 3rd edition of Griffiths' textbook. Ex. 5.8 on page 226 I understand that by reversing the direction of the current, sign of B is switched. but i can't get it that highlighted part. and why B doesn't have z-component? Homework EquationsThe Attempt at...
  4. T

    Instability of a 1D material due to Fermi surface nesting

    Consider the Lindhard response function: \chi(\vec{q})=\int\frac{d\vec{k}}{(2\pi)^d}\frac{f_\vec{k}-f_{\vec{k}+\vec{q}}}{\epsilon_\vec{k}-\epsilon_{\vec{k}+\vec{q}}} where ##\vec{q}## is the wavevector, ##\epsilon## is the free electron energy and ##f## is Fermi-Dirac distribution function. For...
  5. B

    How to cut a surface in ANSYS workbench?

    This is more complicated than it sounds. I'd like to analyse a fracture in a surface body so I need to create a no thickness or infinitesimally small cut/slice if it is possible. Afterwards, I'm planing to analyse stress concentration factor in model environment.
  6. V

    Block moving on a horizontal surface

    Homework Statement Homework EquationsThe Attempt at a Solution Working from the reference frame of block , a pseudo force Ma0 towards right need to be applied on the cylinder . Forces acting on the cylinder are pseudo force , weight Mg and normal force from the block (if any) . Since the...
  7. F

    Find an equation for the tangent plane to a surface (using gradient)

    Homework Statement Find an equation for the tangent plane to a surface xz^2 +x^2y-z=-1 at the point (1,-3,2). Homework Equations (\vec{r}-\vec{r_p}) \cdot \nabla f(\vec{r_p}) = 0 The Attempt at a Solution [/B] First I found the gradient of the function \nabla f = (z^2+2xy)\hat{i} + x^2...
  8. O

    Total Impulse of/on a block pushed along a surface for 10s

    Suppose a block of 5kg is stationary on a table with μ_{s} = .15 and μ_{k} = .1 μ_{s}(F_{N}) = μ_{s}(mg)= .15(5)(10\frac{m}{s^{2}}) =7.5N μ_{k}(F_{N}) = μ_{k}(mg)= .1(5)(10\frac{m}{s^{2}}) = 5NThe force applied to the block is represented by the function: f(x) =...
  9. A

    Exploring the Nodal Surface in 2s Subshells | Insights & Explanations

    why there is a nodal surface in 2s suubshell ?
  10. D

    Why Does the Normal Force Decrease When Pulling Upward on an Object?

    I am trying to solve a homework problem that involves Work and friction but don't understand why if a force pulling upward on the object, the normal force becomes N = mg - Fsin(o) shouldn't it be N = mg + Fsin(o) since both forces are acting upwards? (the normal force and the force applied)
  11. genxium

    How does surface capacitive touchscreen work in detail?

    It's pretty easy to find the "working principle" of surface capacitive touchscreen like http://www.elotouch.com/Technologies/SurfaceCapacitive/howitworks.asp Roughly speaking, I know that A surface capacitive touchscreen has a conductive layer to which some electrodes are attached The...
  12. B

    Where can I buy a flexible capacitive touch surface?

    We need to be able wire it up to a monitor that displays where the surface is being touched. Not a huge feat. However I'd like to start buy ordering a piece a flexible, capacitive touch surface (not a screen). Anyone can assist?
  13. schrodingerscat11

    What does it mean for a surface to be "decorated"?

    In the context of surface science and materials science, what does it exactly mean when a surface is, say, "metal-decorated"? By reading plenty of journals, I am assuming that it means that the atom is adsorbed on the surface, which means that the atom that "decorates" the surface is bonding on...
  14. jorgeavg

    Radiation from the surface of a star

    Hi there, I´m reading about the theory of radiation and came up with some doubts when I started to calculate the net flux that an observer would "see" coming off from the star. I have provided my answers to my own questions but would like to see what you people think about them. 1. Can it be...
  15. gracy

    The flux through the hemispherical surface

    Homework Statement The flux through the hemispherical surface in the figure shown below is Homework Equations The Attempt at a Solution But the above formula is for closed surface .But hemisphere is not a closed surface to make it closed surface we will need another hemisphere . then the...
  16. S

    Evaluate Magnitude of Gravitation at the Surface of a Planet

    1. The trajectory of a rock thrown from a height with an initial speed of 20.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere...
  17. A

    Time dilation on the surface of the sun

    Hi, I am wondering. Is it possible to predict the amount of time dilation on the surface of the sun compared to the surface of the earth? Is this a correct question to ask, or have I made a bad assumption? Thanks in advance. Ayjay
  18. goonking

    Sketch and identify the surface

    Homework Statement 9x2 − 18x + 4z2− 24z − y2 + 45 = 0 Homework EquationsThe Attempt at a Solution so let's start with the zy trace, setting x=0 we are left with: 4z2 - 24z - y2 = -45 completeing the square gives : 4z2 - 24z + 144 - y2 = -45 +144 4(z-12)2 - y2 = 99 divide both sides by 99...
  19. gracy

    Electric flux through open surface

    I know in such type of questions we should try to enclose the charge completely and symmetrically by as many bodies requires as that of the given body. Let's say if Charge Q is kept at the mouth centre of a hemisphere .Here a hemisphere is given so we know if another hemisphere is placed below...
  20. J

    Finding flux through surface where E field is function of x

    Homework Statement In a region of space there is an electric field E(vector E) that is in the x-direction and that has magnitude E=(663 N/(C*m))x Find flux for this field through a square in xy plane at z=0 and with side length 0.330m . One side of the square is along the +x-axis and another...
  21. Legolaz

    Normal and Tangential Component of Vector on a Surface

    Hello, given the figure above, how do I get the tangential and normal components of a vector in any plane by integration?
  22. gracy

    How electric field lines going out from surface is zero?

    in the video above the instructor explains from time 8:22 to 8:55 that how and why electric field lines going out from the surface which do not enclose charge is zero but I don't understand then why not electric field lines going out from the spherical surface ( enclosing charge) is...
  23. J

    How to calculate surface temperature of earth?

    Assumption: Earth is a perfect blackbody. This means that the emissivity (ε) is 1. Earth’s radius = 6371 km Incident solar radiation = 1367 W/m2 Temperature in space = 0 K I'm given the above data. I tried using the E= σεTe4 but that doesn't include the radius of the Earth :S Im really...
  24. caters

    How much does the radius at the surface of the water increase per inch?

    Homework Statement A truncated cone has smaller radius of 5 feet, larger radius of 10 feet, and a depth of 1 foot. Total volume is approximately 183 cubic feet. If I have water in there at x inches how much does the radius at the surface of the water increase per inch? Homework Equations f(x)...
  25. H

    What defines the surface of the Sun?

    The sun has no surface, but it appears to have a surface. I may recall that Feynman said that the apparent diameter is equal to the mean free path of a photon. That could be, but I don't get the relationship. Any help?
  26. Legolaz

    How Do You Calculate the Surface Area of a Helix?

    Hi Forum, Just wanted to ask how to compute surface area of a helix x =cos t, y =sin t, z=t by integration Thanks in advance.
  27. T

    Reference wanted: surface and interface

    I am a Ph.D. student just beginning my research. Recently, I found several papers about surface and interface interesting, so I want to know more about this area. However, I cannot find any specific review which can give me an overview of this area. Can anyone give me a link to such literature?
  28. P

    Are there more flexible formulas for finding the area of surfaces of revolution?

    When I learned about volumes of solids of revolution, I never really memorized any formulas for specific cases per se. I used two expressions for area, either ##A = \pi (R^2 - r^2)## and ##A = 2\pi r h##. Those expressions worked for rotations about any horizontal/vertical axis (not necessarily...
  29. bcrowell

    Is caustic surface of an astrophysical black hole one event?

    MTW, p. 924, defines a caustic as a point where a null geodesic originating from the external universe enters a black hole's event horizon, remaining in the horizon afterward for some finite affine interval. (A null geodesic of this type is called a generator of the horizon.) They introduce this...
  30. Andre

    Average surface temperature independent of radiative gasses?

    http://www.sciencedirect.com/science/article/pii/S0273117715005712 from the abstract: Obviously, the most prominent missing 'forcing' parameter here, is "concentration of greenhouse gasses". There is probably some food for thoughts here, especially when the analysis of Den Volokin and Lark...
  31. Navaraj Baniya

    Surface chrge density on current carrying conductor?

    I am confuse with the fact that current carrying conductor has gradual surface charge density which provide force to electron to produce current.
  32. W

    Why do we use racing slicks if surface area =/= friction?

    I understand how surface area does not come into the equation governing the resistance an object has to sliding. It leads one to believe that all tires would perform equally in dry conditions. Why do people then say that bald tires give better grip?
  33. T

    Electric Field Calculation for Volume and Surface Charges?

    Hello, I know you can use Gauss' law to calculate the electric field of volume and surface charges but i cannot figure out a way to do it using Coloumb's law. I have several questions about this: when you integrate the charge density in Coloumb's law over the volume is the r^2 inside or outside...
  34. D

    How Do You Calculate the Surface Area of a Cone with Equal Diameter and Height?

    Homework Statement Determine a simplified, factorised expression, in terms of the radius (r), for the surface area of a cone where diameter (D) = perpendicular height (h) Homework Equations A = πr (r + √(h^2 + r^2)) The Attempt at a Solution h=D=2r A = πr (r + √(2r^2 + r^2)) A/π = r (r +...
  35. R

    Can a silver atom be physisorbed to its surface?

    Hi all,If there is activation energy for chemisorption, then an atom with insufficient energy to overcome that barrier will remain physisorbed to the surface via van der Waals forces. I would like to further understand this activation energy in terms of, for example, the overlap of electron...
  36. UF6

    How Do You Calculate the Surface Charge Density on a TV Screen?

    Homework Statement You've probably noticed that TV screens and computer monitors have an annoying tendency to accumulate dust. Wanting to understand this better, you decide to model the situation as follows: you assume a small mote of dust might have an excess charge of 1 nC and a mass of 5...
  37. bwilson4web

    Sea level change as ocean surface warms

    Homework Statement I am attempting to replicate the IPCC estimates of the amount of sea level rise due to thermal effects on the seawater. The earth, black-body temperature is 16C but there are projections of a 1C increase in less than 100 years. Ignoring ice melt and land flooding, how much...
  38. U

    Heat equation given constant surface heat flux

    How would I go about finding temperature distribution in a thin square plate during the the first few milliseconds (or actually a fraction of a millisecond) after t=0s. Initial temperature distribution throughout the plate is known, there is heat flux to one side = Qinj, while heat flux from all...
  39. D

    Geodesic Transport of Small 2D Surface on 3D Manifold

    Hello, I've just read and I think I have understood the following result : If we were to geodesically transport all points of a small 2D surface, so small that it would be flat for all purposes, in a direction vertically above it, and if this surface belongs in an arbitrary 3D manifold, then in...
  40. R

    Match on water sustained by surface tension

    Homework Statement A match of length l=4cm is floating on the surface of the water from a glass. ( the water is at room temperature) If from on one side of the match we pour a few drops of soap, the match starts moving. In which direction is the match mooving and what force is acting upon it? (...
  41. Mnemonic

    Cylindrical Gaussian Surface around charged rod

    Homework Statement a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3? b) What is the magnitude of the electric field as a radial distance of r = 20 d? I was able to determine the...
  42. N

    Li ion battery electrode surface area

    What effect (if any) would changing the surface area of electrodes in a lithium ion battery have? Would it allow for faster battery charging? Faster discharge rate? Thanks in advance
  43. C

    Noetherian currents and the Surface term

    When deriving the conserved currents from continuous symmetries, my book states that we can also add a 4-divergence to the lagrangian density which does not change the action under variation. The four divergence can be transformed into a boundary integral by stokes theorem. However, my book...
  44. Stephanus

    Does a black hole have a surface area?

    [Moderator's note: Spin-off from another thread.] I'm sorry, does black hole have surface area? Did you mean the sphere defined by Schwarzschild Radius?
  45. ltkach2015

    Projectile Motion on Inclined Surface Question

    Homework Statement Water is sprayed at an angle of 90° from the slope at 20m/s. Determine the range R. PLEASE SEE ATTACHMENTHomework Equations [/B] Kinematic Equations: acceleration: A = 0i +g(-j) + 0k; velocity: dV/dt = A; position: dR/dt = V; Origin set at the point spout...
  46. K

    Cylinder pulled by rope on a rough surface

    Homework Statement A rope is pulled off with a force F from a combined cylinder. the smaller cylinder's radius is r and the big one's is R. the cylinder rotates on a rough surface without sliding. the force makes an angle θ with the horizon. What's the acceleration's "a" magnitude and...
  47. T

    What software for optimization surface of 4 parameters?

    Hello, I have data for optimization that contains different values of 4 different parameters, and the respective function value based on them. I want to find the maximum of this function, while making sure it's a "stable" maximum, i.e., for nearby parameters, the value of the function shouldn't...
  48. B3NR4Y

    What is the purpose of a surface integral and how is it calculated?

    I'm beyond multi-variable calculus, where this is taught, but I still don't know what the hell a surface integral is. I understand that d\sigma is the surface element, and | \frac{\partial \vec{r}}{\partial u}du \times \frac{\partial \vec{r}}{\partial v}dv | = d\sigma = |\frac{\partial...
  49. A

    Tension force and a board fixed to a flat surface

    A heavy board is fixed to another flat surface along its entire upper edge and not moving. How can I find the tension force that is acting on the board? Is it the same as if the board would be fixed to a string in the middle of the upper edge and hung and then the tension would be T=mg?
  50. U

    Total derivative involving rigid body motion of a surface

    This stems from considering rigid body transformations, but is a general question about total derivatives. Something is probably missing in my understanding here. I had posted this to math.stackexchange, but did not receive any answers and someone suggested this forum might be more suitable. A...
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