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. S

    Magnetic field of plane with thickness d with uniform surface current

    I'm confused what's meant by a uniform surface current density since this plane has a thickness, It would need a current density distributed through its cross sections, I thought.Edit: I tried solving with proper LaTeX and all my steps, but it looked awful. For outside, I got B=µ_0jd/2. for...
  2. Wesleyk89

    Extend Magnetic Field Density from magnetic object's surface?

    I am new to the site I apologize If I am posting incorrectly or doing something wrong. I need help figuring out how to increase magnetic field density (gauss/tesla's) extending from a magnetic object's surface, most magnets magnetic density is all in the center. I need this in order to induce a...
  3. LCKurtz

    Insights Demystifying Parameterization and Surface Integrals

    Continue reading...
  4. E

    Surface area to volume ratio

    In a human body we have two relatively similar structures -pulmonary...
  5. L

    Pressures distribution: solid sphere on a flat surface

    In a real case (not ideally rigid bodies), a (e. g.) hard metal sphere is on a flat (e. g.) hard metal surface (a table) and the sphere is "charged" vertically on the table by a vertical force directed downward. In this situation, an engineer told me that the maximum pressure on the table is not...
  6. F

    Orbital velocity of a craft at 4km above the Moon's surface

    What would be the orbital velocity of craft at 4km above moon surface? Assume a mass of 1,000,000 lb, US.
  7. M

    I Why do we ignore the contribution to a surface integral from the point r=0?

    Let ##V'## be the volume of dipole distribution and ##S'## be the boundary. The potential of a dipole distribution at a point ##P## is: ##\displaystyle\psi=-k \int_{V'} \dfrac{\vec{\nabla'}.\vec{M'}}{r}dV' +k \oint_{S'}\dfrac{\vec{M'}.\hat{n}}{r}dS'## If ##P\in V'## and ##P\in S'##, the...
  8. T

    I Proving radial properties of particular dimensionless surface plots?

    We have a surface function z = f(x,y) ; f(x,y) only contains dimensionless constants, and is itself dimensionless. If we convert it to cylindrical co-ordinates, z = f(r,θ) , does z only depend on θ? Meaning we can remove r from the equation, literally.
  9. JD_PM

    What are the limits of integration for this surface integral?

    I want to compute: $$\oint_{c} F \cdot dr$$ I have done the following: $$\iint_{R} (\nabla \times v) \cdot n \frac{dxdy}{|n \cdot k|} = \iint (9z-1) dxdy$$ I don't know what limits the surface integral will have. Actually, I am not sure what's the surface. May you shed some light...
  10. P

    Is Ball Bouncing on a Surface a Simple Harmonic Motion?

    Answer is C.
  11. N

    Surface Rayleigh waves generation

    Good day, I do not fully understand the physical mechanism of formation of Rayleigh waves at the free surface. While their derivation is quite clear and obey free-boundary conditions, it is not clear their physical mechanism. Could you please correct me in my discussion. Incident P-wave can...
  12. JD_PM

    Understanding the argument of the surface area integral

    Homework Statement Find ##\iint_S ydS##, where ##s## is the part of the cone ##z = \sqrt{2(x^2 + y^2)}## that lies below the plane ##z = 1 + y## Homework EquationsThe Attempt at a Solution [/B] I have already posted this question on MSE...
  13. JD_PM

    Understanding why we compute surface area as we do

    Homework Statement Homework Equations The Attempt at a Solution [/B] The solution to this problem is known. I want to use this exercise as a model to understand how to proceed when calculating the surface area of a geometric figure. Question: 1) Why do we differentiate with...
  14. T

    Some questions about surface plasmon polaritons

    Hi there, To be clear, this is not a homework question, I am a graduate student reading about the use of plasmonics for biosensing. I felt I should post here instead of in the "general physics" forum since I do have questions, but they are more qualitative, nonetheless I will try to follow the...
  15. QuarkDecay

    Flow (liquid or gas) across a rotating surface's face

    << Mentor Note -- Two threads on the same question merged into one thread >> How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades? Example, when it falls vertically to the blades, it's Pmax= 8/27Sρu13 But if there's for...
  16. G

    Surface temperature of a Cylindrical heated rod

    How can I calculate the surface temperature of a Cylindrical Heating rod after some time interval? There is internal heat generation in the rod and convective heat transfer to the surroundings.
  17. V

    B Solving an Integral on a Spherical Surface - Tips

    Hello. I ask for solution help from the integral below, where y and x represent angles in a metric of a spherical, 2-D surface. He was studying how to obtain the geodesic curves on the spherical surface, the sphere of radius r = 1, to simplify. The integral is the end result. It is enough, now...
  18. CharlieCW

    Force of a magnetized cylinder on a ferromagnetic surface

    Homework Statement A long straight cylinder with radius ##a## and length ##L## has an uniform magnetization ##M## along its axis. (a) Show that when its flat extreme is placed on a flat surface with infinite permeability (i.e. a ferromagnet), it adheres with a force equal to: $$F=8\pi a^2 L...
  19. JD_PM

    Average electric field over a spherical surface

    Homework Statement I was working out problem 4, chapter 3 of Introduction to Electrodynamics by Griffiths: a) Show that the average electric field over a spherical surface, due to charges outside the sphere, is the same as the field at the centre. b) What is the average due to charges inside...
  20. C

    Enzymatic surface for multistep reactions

    Is it possible to create a surface with immobilised enzymes (or any other technique) that will perform a multistep reaction?
  21. confusedius

    Solid State Physics: Draw the Dispersion Relation from the Fermi Surface

    Homework Statement ln the figure below you (b, which is taken from Jenö Sólyom Fundamentals of the physics of solids. Volume 2 chapter 19) see the Fermi sphere of radius k_F inside one section in two dimensions of the Brillouin zone of Na. Draw the dispersion relation E(k) from the I point in...
  22. L

    Minimal surface area for a fixed volume

    Homework Statement a hut has to side walls a roof and back wall. its front is open. its total volume is 120m^3 fdetermine the miniumal surface area necessary for a sheet to be put over it Homework EquationsThe Attempt at a Solution Attempt 2 V=xyz=120 z=120/xy s = 2yz + xz + xy s = 2y(120/xy)...
  23. Specter

    Minimizing the surface area of an open box

    Homework Statement An open topped box with a square base has the capacity of ##32m^2##. Find the dimensions that will minimize the surface area of the box. Homework EquationsThe Attempt at a Solution I was told these are the dimensions, but I can't picture them in my head at all...
  24. A

    Variable induced surface charge density on a sphere

    Homework Statement Homework Equations While solving this problem at r >>a ,the corresponding potential due to the dipole is kpcosθ/r2(potential due a dipole) where k is the electrostatic constt. ...(1) If σ(θ) is the surface charge density induced due to external electric field. then the...
  25. A

    How does the dielectric affect the charge distribution on a charged sphere?

    Homework Statement [/B]Homework Equations [/B] ∫Dperpendiculards=qenclosed freecharge D=ε0E+P The Attempt at a Solution D1+D2=q/2πr2 at a distance r from the centre How to find D2 which is at the lower boundary e.g inside the dielectric??
  26. M

    Surface area of a shifted sphere in spherical coordinates

    Homework Statement find the surface area of a sphere shifted R in the z direction using spherical coordinate system. Homework Equations $$S= \int\int \rho^2 sin(\theta) d\theta d\phi$$ $$x^2+y^2+(z-R)^2=R^2$$ The Attempt at a Solution I tried to use the sphere equation mentioned above and...
  27. Raihan amin

    Induced surface charge distribution

    Two identical metalic spherical conductor of radii ##R## are at a distance ##d## apart.One of the conductor has charge ##Q## while the another one is neutral.What will be the induced charge on the other conductor ? If we put an image charge ##q## inside the neutral one. Then the potential at...
  28. W

    Find the curve with the shortest path on a surface (geodesic)

    Homework Statement Let ##U## be a plane given by ##\frac{x^2}{2}-z=0## Find the curve with the shortest path on ##U## between the points ##A(-1,0,\frac{1}{2})## and ##B(1,1,\frac{1}{2})## I have a question regarding the answer we got in class. Homework Equations Euler-Lagrange ##L(y)=\int...
  29. iVenky

    Surface charge on a conductor due to a charged rod 'q'

    Homework Statement A charged rod of charge 'q' is at a distance 'd' from a perfect conductor as shown below. What's the total surface charge on the conductor? 2. Homework Equations I tried to solve this without equations. The Attempt at a Solution [/B] Basically, as long as there is E field...
  30. gibberingmouther

    I Is There a Curve For a Material's Surface Area vs. UTS

    I drew a diagram in order to help figure out something for a tabletop game I'm putting together. My question is about the physics of materials, and is not directly about the fictitious psychic/magic abilities in my game world. I drew a diagram consisting of dots representing particles and...
  31. A

    B Positive curvature of a 2D surface

    If considering a 2D surface (plane) having polar coordinate r,θ (where r is the distance from the origin and θ is the anticlockwise angle from the base line as usual) The metric is now actually ds2=dr2+r2dθ2 If now this 2D surface is given a positive curvature of +1 (equivalent to the surface of...
  32. P

    Explaination of Solid-Liquid and Solid-gas surface tension

    I am a high school student and currently studying Mechanical properties of fluid. We are taught surface tension in a very introductory level and most of it is about liquid-gas surface tension. We are taught that liquid-vapour tension is the atrractive forces that water molecules experience at...
  33. P

    Surface tension in terms of temperature and concentration of an added substance

    Hi! Here's a tricky thermodynamics problem, I hope you can help with it. 1. Homework Statement The boundary between two different materials can be divided into two different kind of phases: bulk phases and surface phases. For example, let's consider a boundary between water and air. We can...
  34. L

    Calculating the wavelength of a surface wave after impact

    Homework Statement There's a bucket, filled about halfway with water. The water itself is completely still. A perfect sphere with mass m and volume v are given. The depth of the water, and the radius of the bucket (which may be considered perfectly cylindrical) are both given. In short, you...
  35. Benjamin Fogiel

    A rocket burns out at an altitude h above the Earth's surface

    Homework Statement A rocket burns out at an altitude h above the Earth's surface. Its speed v0 at burnout exceeds the escape speed vesc appropriate to the burnout altitude. Show that the speed v of the rocket very far from the Earth is given by v=(v02-v2esc)1/2 Homework Equations KEf-KEi=Ui-Uf...
  36. Boltzman Oscillation

    How would I perform this surface integral?

    Homework Statement ∫∫ F ⋅ ndτ over the spherical region x^2 + y^2 + z^2 = 25 given F = r^3 r i already converted the cartesian coordinates to spherical in FHomework Equations n = r[/B]The Attempt at a Solution I know I can plug in F into the equation and then dot it with r to get the...
  37. G

    I Rippled surface on lake ends abruptly

    Hi. I've made these pictures on Reichenau Island in Lake Constance, Germany. I was suprized about that clear line between the calm area close to the shore and the more rippled surface further out. The wind was weak, but directed from water to land. From a pier I could see that the ground drops...
  38. Logic hunter

    Calculating the pressure on a surface exerted by opposing forces?

    Suppose there is a circle with area 'A' and on one of the faces of the circle a force of 100N is applied and on the other face a 30N force is applied (since all 2D surfaces have 2 faces) such that these forces are opposite to each other, perpendicular to the faces, and forces are equally...
  39. A

    Calculating surface tension with the Capillary Equation

    Homework Statement Hello everyone, I am doing an experiment and I've hit a snag with my calculations. I am looking at how concentrations of soap affect surface tension in water. I am have been using the capillary equation and capillary tubes for my calculations. I have practiced this method for...
  40. R

    Average Pressure Radiation on Perfectly Absorbing Surface

    Homework Statement A light source radiates a sinusoidal electromagnetic wave uniformly in all directions. This wave exerts an average pressure p on a perfectly reflecting surface a distance R away from it. What average pressure (in terms of p) would this wave exert on a perfectly absorbing...
  41. D

    Bound surface charge on a linear dielectric half-cylinder

    Homework Statement Problem statement in attached photo. This is an ungraded assigned problem which I am using to study for an exam, so I don't need the whole solution just help with a couple of points I am confused about. One: Part d) is really important to how I will answer part b). If we can...
  42. Akash47

    Block at rest on an inclined surface

    Homework Statement Homework Equations Component of force,equilibrium of force. The Attempt at a Solution In the problem (ii),the friction force is ##Mgcosθμ##,the component of weight in the inclined surface is ##Mgsinθ## and the component of the applied force ##F## along the inclined surface...
  43. EelAnes

    What is the coefficient of drag on a flat surface?

    What is the coefficient of drag on a flat surface? Note: The body is in free fall The object has 2 wings planform (it's a paper helicopter), which is flat The object's wing spin in a circular motion (anti-clockwise) during free fall
  44. Q

    The minimum inclination of a surface

    I am an IT student and working on a project, an automated system. It's not for a physics class. I can't say exactly what the system can do. But it uses Arduino to dispense servings of grains on a given schedule. I am more of a programmer than a physicist, I am looking for help on this. 1...
  45. D

    I A surface integral over infinite space

    Hi. If a function f is normalizable ,ie f→0 as | x | → infinity or r→ infinity then I presume the following surface integral f dS over infinite space is zero ? But I thought about this again and it seems like a case of zero x infinity. The function is zero at the infinite surface but the area...
  46. A

    What do surface tension vectors mean in this quote?

    I was reading Fundamentals of Inket Printing and it said the following: "The surface tension in a liquid causes a force to act in the plane of the free surface perpendicularly to a free edge in that surface." Can someone explain to me what this means? What's the direction of the force? I have...
  47. Eric Bretschneider

    Emission of light from a surface

    I came across someone in the lighting industry who insists that because of Gauss's divergence theorem and Maxwell's Laws that when light is emitted from a surface that it is only emitted orthogonal to the surface. I have tried to point out numerous real world examples that contradict the...
  48. S

    Simulating shape of spinning water surface

    I would like to simulate a simplified version of this phenomenon: where I will assume that the viscosity is zero and the liquid can therefore swirl around "laminarly" forever according to some velocity profile that I specify. How can I calculate the shape of the surface, at least in this...
  49. nmsurobert

    I "Surface" gravity of gas giants

    I just read a couple articles discussing the surface gravity of Saturn and Jupiter. I would expect the "surface" gravity of these planets to be much higher than that of Earth. I understand how the low densities of these planets has influence on that, but I thought mass was related to gravity in...
  50. shk

    Gravitational Potential Energy questions near the surface of a planet

    Homework Statement The change in gravitational potential energy of a mass m as it moves from the surface to a height h above the surface of a planet of mass M and radius R is given by: ΔPE= GMmh/R(R+h) a) show that when h is very small compared to R , this approximates to the more familiar...
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