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. thecourtholio

    Distance to surface of last scattering in +, -, and flat uni's

    Homework Statement 1) Calculate the angular diameter distance to the last scattering surface in the following cosmological models: i) Open universe, ΩΛ= 0.65, Ωm = 0.30 ii) Closed universe, ΩΛ = 0.75, Ωm = 0.30 ii) Flat universe, ΩΛ = 0.75, Ωm = 0.25 Describe how the CMB power spectrum...
  2. A

    Conical Surface Potential Difference

    Hey guys! The question is related to problem 2.26 from Electrodynamics by Griffiths (3ed). 1. Homework Statement A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, as the radius of the top. Find the potential difference between points a...
  3. Destroxia

    Surface Area of Parameterized Region

    Homework Statement Find the surface area S of the portion of the hyperbolic paraboloid: ## r(u,v) = \langle (u+v),(u-v),uv \rangle ## for which: ## u^2 + v^2 <= 225 ##Homework Equations (Surface Area for Parameterized Region:) ##\int \int ||\frac {\partial r} {\partial u} \times \frac...
  4. CGMath

    Parametrization for Surface F and Area A

    An area A in the (x,y) plane is limited by the y-axis and a parabola with the equation x=6-y^2. Further, is a surface F given by the part of the graph for the function h(x,y)=6-x-y^2 which satisfies the conditions x>=0 and z>=0. Determine a parametrization for A and for F. So far I've got the...
  5. M

    A Electrostatic Repulsion of graphene layer on metal surface

    Dear Member, Respected Members, I am working on the behaviour of hydrogen at the Cu/Ni (111)-graphene interface. In case of Ni (111), the atomic H on the interface diffuse inside the the surface. While in case of Cu (111), the H atom stays at the Cu(111)-graphene interface. It seems that H...
  6. Thales Costa

    I Parameterize an offset ellipse and calculate the surface area

    I'm given that: S is the surface z =√(x² + y²) and (x − 2)² + 4y² ≤ 1 I tried parametrizing it using polar coordinates setting x = 2 + rcos(θ) y = 2rsin(θ) 0≤θ≤2π, 0≤r≤1 But I'm not getting the ellipse that the original equation for the domain describes So far I've tried dividing everything...
  7. lasisdabomb

    Calculate the Average Surface Temperature of Earth

    Homework Statement The Earth receives on average about 390 W m−2 of radiant thermal energy from the Sun, averaged over the whole of the Earth. It radiates an equal amount back into space, maintaining a thermal equilibrium that keeps the average temperature on Earth the same. Assuming the Earth...
  8. Titan97

    Surface charge density of conducting disc

    Homework Statement This is problem 3.4 from Prucell and Morin if you have the book. Homework Equations None The Attempt at a Solution Electric field inside a conducting sphere is zero. Let P be a point on one of its equatorial plane. The field along the plane is zero. So I know the charge...
  9. A

    A Project img on X-Y surface to a cylinder placed in center....

    Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...
  10. Anakratis

    Bubble dynamics over a liquid surface

    Hey all, Interestingly enough, I was actually recently feeding some ducks at a nearby pond when I noticed a cool phenomenon that I couldn't explain myself, so I was hoping you guys could assist in that. When you have two air bubbles over a liquid surface, like water, they seem to accelerate...
  11. T

    Why Do We Subtract Densities in Surface Tension Calculations?

    From a textbook: I don't quite understand the part where the difference of densities is taken, could someone explain that for me? Thanks.
  12. G

    I Drawing a Continuous Symmetrical Grid on a Sphere's surface

    The motivation for this thread comes from physics, but I'm posting it in the maths section as the question is more of a mathematical one and less concerned with the underlying physics. In cosmology, they often talk about closed universes with positive curvature, or non-Euclidean elliptic...
  13. Matt atkinson

    Free Particle on spherical surface

    Homework Statement By finding the Lagrangian and using the metric: \left(\begin{array}{cc}R^2&0\\0&R^2sin^2(\theta)\end{array}\right) show that: \theta (t)=arccos(\sqrt{1-\frac{A^2}{\omega^2}}cos(\omega t +\theta_o)) Homework EquationsThe Attempt at a Solution So I got the lagrangian to be...
  14. R

    What is the surface current density at a general point on a conducting sphere?

    Homework Statement Electric current of I amperes flows along the z-axis from (0, 0,-∞) to (0, 0, -a) and from there it spreads over a conducting sphere r = a in the -aθ direction, comes to the point (0; 0; a) and goes to (0, 0, ∞) again along the z-axis. What is the surface current density at...
  15. rolotomassi

    I Lagrangian - surface of sphere

    I have a free particle moving on the surface of a sphere of fixed radius R. Gravity is ignored and m/2 is left out since its constant. The lagrangian is L = R^2 \dot{\theta^2} + R^2 sin^2{\theta} \dot{\phi^2} Using the Euler Lagrange equations I obtain sin^2{\theta} \dot{\phi} = A = const \...
  16. P

    Free falling particle near Earth's surface (Diff. Eq.)

    Homework Statement The free fall acceleration of a mass ##m## above the Earth's surface in one dimension can be represented by ##m\ddot{y}=-\frac{mMG}{y^2}## where ##M## is the mass of the Earth and ##G## is the gravitational constant. With ##\dot{y}(t=0)=0## and ##y(t=0)=y_0##.. (1) Find an...
  17. DeathCheese

    Calculate force on Permanent Magnet near a Paramagnetic surface

    Hello all, new here but plan to stick around for a while. I am currently trying to make a sensor that can detect if a material below it is paramagnetic. I believe paramagnetic is the proper term, but it needs to detect if the force exerted by permanent magnet is above a certain threshold. The...
  18. F

    Ball bounce angle on inclined surface

    Homework Statement Ball strikes inclined plane of infinite mass with velocity v vertically. Elastic collisions. Velocity and direction after collision? One way of solving is take components along and perpendicular to inclined plane and then solve easily. Is there any way to solve is using...
  19. W

    Understanding Forces on Submerged Surfaces

    Homework Statement i don't understand the statement 1 and 2 , can someone help to explain ? for 1 , does the author mean Fh= Fv ?? for 2 , does the author mean Fv = Fh + W ? but in statement 1 , Fh already = Fv Homework EquationsThe Attempt at a Solution
  20. K

    Gaussian surface (infinitely long cylindrical conductor)

    Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...
  21. I

    Electric field outside a gaussian surface

    Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...
  22. K

    Why stress is defined on 3 surface

    https://www.google.ca/search?q=stress&biw=1366&bih=629&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjA9u3S5_jKAhXCJx4KHfN8DmYQ_AUIBigB#tbm=isch&q=stress+tensor&imgrc=xK8-tGSPxXha7M%3 This is a simple question. -why stress is defined on 3 surfaces only instead of the entire 6 surfaces? I believe 3...
  23. Crush1986

    Question about Riemann Surface Problem

    Homework Statement f(z)=z^\frac{3}{2} find the branch points, branch cuts, and Riemann sheet structure. Homework Equations none The Attempt at a Solution So, I converted this to complex exponential form r^\frac{3}{2} e^\frac{i*3*\Theta}{2} From here I mapped around a circle that was...
  24. Z

    Where are the electrons near Fermi Surface spatially distributed in HTS

    Namely, are the wave functions of electrons near the Fermi surface spatially distributed in the so-called "active blocks" (CuO2 layers and etc.) or in the so-called "charge reservoir blocks" ? Or any other case? ( EO/(AOx)m/EO with m =1, 2 monolayers of a quite arbitrary oxide AOx(A = Bi, Pb...
  25. Y

    What is the magnitude of the net charge enclosed by surface?

    Homework Statement A closed surface with dimensions a = b = 0.302m and c=0.604m is located as in the figure. The electric field throughout the region is nonuniform and defined by E⃗ = (α+βx2)ˆı where x is in meters,α=4N/C, andβ=4N/(C·m2).? What is the magnitude of the net charge enclosed by the...
  26. W

    Simple Surface Integral - Heat Flow on Surface of Star

    Homework Statement I have this problem in an online assignment. Someone told me the answer, so I already got it right, but I don't know why my logic leads me to the wrong answer. The problem: The temperature u of a star of conductivity 1 is defined by u = \frac{1}{sqrt(x^2+y^2+z^2)}. If the...
  27. A

    Surface brightness and effective radius

    Homework Statement Assuming that the average surface brightness within the effective radius is 19 mag/arcsec2, use the definition of the effective radius to estimate what the effective radius in kpc would be for NGC 4216 if it was an elliptical galaxy. Homework Equations All the logs are base...
  28. N

    Diffusion across surface with constant temperature

    Homework Statement A Ti Rod is to be put into a furnace to try and increase the carbon content of the rod. Initially, the carbon content of the rod is 0.2%wt. The carbon content of the furnace is 1.0%wt. What would the temperature have to be in order to get a final carbon content in the Ti rod...
  29. gracy

    Electric Pressure on a Charged Surface due to External EF

    Why he did not consider parallel force?Will parallel component of electric field not produce electric pressure on the surface?
  30. woprxcpe1704tks

    Hollow Sphere with Uniform Surface charge

    Homework Statement [/B]Homework Equations Poynting's Theorem S = 1/μ0 (E x B) Momentum = p = μ0ε0 ∫ S dτ The Attempt at a Solution My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the...
  31. A

    Does Gauss' Law use line integrals or surface integrals?

    In my physics textbook, I see Gauss' Law as https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png\ointE dA but in other places I see it as...
  32. A

    Hurricane reduction through ocean surface cooling

    Old article: http://edition.cnn.com/2009/TECH/science/08/28/hurricanes.gates.gray/ What do you guys think? Where do you see this project going? The official word is that it's not being publicly funded. But if there was even a 10% chance it would work, I see governments lining up at the...
  33. P

    Surface Integrals: Evaluate A.n dS on 2x+y=6 Plane in 1st Octant

    Homework Statement Evaluate integral A.n dS for A=(y,2x,-z) and S is the surface of the plane 2x+y=6 in the first octant of the plane cut off by z=4 Homework Equations Integral A.n dS The Attempt at a Solution The normal to the plane is (2,1,0) so the unit normal vector is 1/sqrt3 (2,1,0)...
  34. M

    Surface area of a spherical cap by integration

    hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...
  35. M

    MHB Calculation of a surface integral

    Hey! :o I want to calculate the surface integral of $$F(x,y,z)=(0,0,z)$$ on the unit sphere with parametrization $$x=\sin u \cos v, \ y=\sin u \sin v , \ z=\cos u \\ 0\leq u\leq \pi, \ 0\leq v\leq 2\pi$$ with positive direction the direction of $T_u\times T_v$. Could you give some hints how...
  36. M

    Hydrostatic Pressure Curved Surface

    Hi PF! I have been reading and reading for a clean explanation for the hydrostatic force of a curved submerged 2-D (or 3-D if you're up to it) surface. I really don't care what the curve looks like: quadratic, circular, partway sinusoidal, etc. All articles I read involve the centroid, but...
  37. G

    Destructive interference at a surface

    Take two lasers of the same intensity and wavelength and aim them at 30 degrees at the same spot on a mirror, so that at the surface the waves cancel perfectly. What happens? How can the wave be reflected if there is no field present?
  38. C

    Is there always a liquid surface between a solid and gas?

    So I'm reading that ice (solid) always has a liquid surface if it's surrounded by a gas. Does this mean every solid (e.g., my dining room table) also has a liquid surface because it's surrounded by gas? It doesn't seem to have a liquid surface. :-/ If something sublimes it skips this phase so I...
  39. A

    Aerostat on Venus vs Surface Colony on Mars

    Idk where i picked this up, but there is one other plausible colony destination for humans: Venus. After a few trips on the net, I've come to the "Aerostat on Venus" side instead of a colony on mars. I'll mention some of the reasons I've picked up as to why: 1. Tons of CO2, we can use that. 2...
  40. C

    A rod falling on a frictionless surface

    Homework Statement Consider a massless rod of length $L$ with a small mass $m1$ attached on one end, and $m2$ attached on the other end. The rod is initially in the vertical position at rest on a frictionless surface, with $m1$ on bottom and $m2$ on top. A small impulse is applied to the top...
  41. P

    Localized surface plasmon resonance (LSPR)

    Hi! I wondering does anyone here has a clue of lowering the absorption level and narrowing the scattering bandwidth of LSPR of nanoparticles? Are those "intrinsic" properties or can be improved by modifying their size, shapes, etc? Thanks for sharing your thoughts! Paul
  42. P

    Area of z^2=xy inside Hemisphere: Surface Integrals

    Homework Statement Find the area of the part of z^2=xy that lies inside the hemisphere x^2+y^2+z^2=1, z>0 Homework Equations da= double integral sqrt(1+(dz/dx)^2+(dz/dy)^2))dxdy The Attempt at a Solution (dz/dx)^2=y/2x (dz/dy)^2=x/2y => double integral (x+y)(sqrt(2xy)^-1/5) dxdy Now I'm...
  43. N

    Why is low surface energy important for water droplets on hydrophobic surfaces?

    a thin film of water has surface tension due to the strong bonds present on the surface in order to counteract the net downward force and this increases the potential energy of the surface layer of particles therefore on a hydrophobic surface it forms a water droplet , my question is since it...
  44. P

    Flux integral over ellipsoidal surface

    Homework Statement I am having trouble with part iii) of the following problem: Verify the divergence theorem for the function ##\vec{u} = (xy,- y^2, + z)## and the surface enclosed by the three parts: (i) ##z = 0, x^2+y^2 < 1##, (ii) ##x^2+y^2 = 1, 0 \le z \le 1## and (iii)...
  45. JoAstro

    Surface temperature of a star?

    I am trying to find the temperature of a star given its wavelength in micrometres, but I am not sure if my conversion is right therefore don't know if the answer is correct. Star A has a maximum emission wavelength of 1 μm and Radius 100 Rsun. What is its Effective Temperature and Luminosity...
  46. G

    Formula of weight of surface water

    Homework Statement Why the weight of water at water surface is given by formula 2(pi)Rσ(cos angle) ? Homework EquationsThe Attempt at a Solution
  47. J

    Surface States within band gap STM/STS

    Hi there people! So my question is why you can see localized surface states within the band gap of the material with an STM. How is a tunneling circuit being established?
  48. S

    Intersection of general plane with quadric surface

    So far I have calculated this for a cone, which elegantly results in the conic sections. However, I would like to do this for the other quadric surfaces. Is the calculation for this been published anywhere online?
  49. H

    A car stopping on a slippery surface on an uphill

    Let's say we have a car going up a 10% grade that slams on the brakes. The normal force would be mg(cos angle of elevation) in a component of Fg that is perpendicular to the road surface, and there would be a direct effect of gravity in the component of Fg that is parallel with the road...
  50. T

    Distributing weight of four legs evenly over surface

    I have a stepper exercise machine that stands on four legs and I would like to place this machine on a shelf made of canvas cloth ( the whole wardrobe is made of canvas ). The problem is I think the shelf would tear where the four legs are. So I would like to ask if there is any way I could...
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