Surface Definition and 1000 Threads

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. L

    Surface integrals of vector fields, normal - does scaling matter?

    Source: https://tutorial.math.lamar.edu/Problems/CalcIII/SurfIntVectorField.aspx Alright so my confusion lies in the following step: Consider the side x = 0. Okay, from the formula (I am just going to insert an image here) Okay, so gradient of f would just be <1, 0, 0>, which is simply i...
  2. L

    I Increase in surface charge density in different frames of reference

    I am reading Purcell's Electricity and Magnetism and am getting confused on equation 5.22. It seems to me they are using relativistic velocity addition for u' which is u'=(u-v)/(1-uv/c^2), but aren't we solving for the velocity of the electrons in the test charge's frame of reference, so should...
  3. S

    4D Poincare surface of sections

    Can anyone help me with this? I have posted my code at the below: https://mathematica.stackexchange.com/questions/306820/4d-poincare-surface-of-sections
  4. squeak83

    B Vacuum surface area balance and force

    Evening all, im not exactly sure where this lies in the prefix, so apologies if it is higher than that. I am trying to figure out a device that uses fan vacuum and suction seal, and a little bit of ground effect with a fan to adhere to objects, I'm by no means a learned man, and i was...
  5. Sidsid

    B-field from a current in a wire above a conducting surface

    I first thought of imaging techniques, because the setup reminded me of it, but i have only ever seen those of electrostatics. If i for example add a current in the opposite direction and with the opposite heigth of the surface the fields dont cancel out at the surface, i think. What is the best...
  6. A

    I Question about Integrals to Determine Volume vs Surface Area

    I'm a little thrown off with material I'm going through right now. I already covered the whole "area under the curve" and using that to determine the volume of a given equation, but I'm confused now as to why calculating the surface area has a different method with ds? For example, say there...
  7. P

    Contact Mechanics: Deformation of a ball on a surface

    A solid ball of radius R, density ρ, and Young’s modulus Y rests on a hard table. Because of its weight, it deforms slightly, so that the area in contact with the table is a circle of radius r. Estimate r, assuming that it is much smaller than R. I have no issues understanding the...
  8. P

    Oxygen and hydrogen atoms on the diamond's surface

    Is it true that hydrogen and oxygen atoms on the surface of diamond make it have such a low coefficient of friction?
  9. Z

    Derive surface brightness formula

    Derive formula for surface brightness The formula in question we wanna derive is: S(mag/arcsec^2) = M⊙ + 21.572 -2.5 log_{10} S(L⊙/pc^2). Best regards.
  10. L

    Shape of equipotential surface in 3d

    We have 2 infinite cylinders, need to find out which shape will equipotential surface be in 3D.
  11. PhysicsEnjoyer31415

    I What is Surface Plasmon Resonance?

  12. Antarres

    A A question about an 'extremal' surface

    I'm not sure this is a differential geometry question, but I think it is. In general when we have a hypersurface(or in case of 3D space just a surface) it is defined with an equation ##f(x^a)=0## for some function ##f##. Then the normal vector is the gradient of this function, if we want an...
  13. marciokoko

    Surface area of inclined XY plane at 45 degrees

    Is it just sqrt2?
  14. druscilla

    Rate of EM emission based on surface characteristics

    I would think the black painted surface is
  15. H

    Forces for bodies connected by a wire on inclined surface

    Hello PhysicsForums! Here is my attempt at a solution for the problem stated above: Where m1 and m2 are the masses Where Ff1 and Ff2 are friction for each mass Where a1 and a2 is the resulting acceleration Where S is the fore of the wire (threadforce) Where FN is the normal force The answear...
  16. Xiothus

    Solve First Year Harmonic Motion Problem: Cylinder Rolling

    Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems. Have a wonderful day, again thank you for checking this post out!
  17. B

    B Water surface behavior under pressure change

    Hi togehter, this may be an easy one for most, but I'm really struggling with imagining the process. Suppose we have a compressed air vessel that is half filled with water. The pressure in the vessel drops from 10 bar to atmospheric pressure within a few seconds. How does the water surface...
  18. Mohmmad Maaitah

    Find tension in ropes connecting 3 masses being pulled on a surface

    This is the problem and my answer below it. my friends said it's 250 N and I say it's 100 N based on what I solved what am I missing ?? my try:
  19. V

    Equipotential surface (test questions)

    The answer to the first question should be a sphere since for very large distances the multiple charges will act as a point charge. 1(a) is correct answer. For the second question, I find it slightly vague. How can equipotential surface be zero, may be it's asking for the potential of...
  20. simito_

    I Surface area and length (percent increase relationship)

    Hi all, While calculating the surface area for an object, I was told the below statement. However, I am not sure is this correct, please can someone help me to explain this with an example? Is the below statement always true? The surface area % increase should be in line or less than the %...
  21. Justforthisquestion1

    Pulling a yoyo over a surface with tension

    My Work so far: So there is a Force F applied to the right and since we have a no slipping condition we have a static friction force fs to the left. So the only thing that can move the center of mass (cm) of the yoyo is rotation. F would lead to a ccw rotation and fs to a clockwise rotation...
  22. bo reddude

    What are the forces on a cell in a tree vs on the surface of a tree

    Hey everyone. Let's say you have a tall tree. say, 10 m tall. Take a cubic cell 1mm in dimensions. Suppose the cell is at 1 m high in the center of the trunk of the tree. What are the forces acting on the cell? let's say tree cell's mass is t grams. its weight is F= ma = t (9.8) = 9.8 t...
  23. 1

    MCNP6.2 - SDEF on a RCC surface

    Hi everyone, I'm trying to set up a surface neutron source on the surface of a cylinder defined as a macrobody (RCC) and used also to define cell of the system. My aim is setting up a surface source where I'd like to give a specific spectrum (and DIR) at each surface defining the cylinder...
  24. ergospherical

    Electrons escaping a metal surface

    In the low temperature limit ##\mu \approx E_F## and the Fermi-Dirac distribution is ##n(E) \approx g(E)/(e^{\beta(E-E_F)}+1)##. An escaping electron contributes ##\Delta j_z = -ev_z = -ep_z/m## to the current density. How can I calculate the rate that electrons escape at? I can't see how to...
  25. E

    Electron encountering metal surface (1D Step potential)

    I am struggling with how to go about this; in particular, I'm not sure I understand what state is being alluded to when Ballentine says "For an electron that approaches the surface from the interior, with momentum ##\hbar k## in the positive ##x## direction, calculate the probability that it...
  26. Cringle

    Downdraft table -blocking off part of table surface to increase flow?

    Hello everyone. First post! I am struggling to understand an issue in our (histology) lab. We use large downdraft tables which extract the noxious substances we use, mainly formaldehyde, while we process surgical samples. These tables have a steel cover with lots of holes about 5mm diameter...
  27. rokiboxofficial Ref

    Surface density of the charges induced on the bases of the cylinder

    The correct answer to this problem is: ##\sigma = \varepsilon_0E\frac{\varepsilon-1}{\varepsilon}## Here is my attempt to solve it, please tell me what is my mistake? ##E_{in} = E_{out} - E_{ind}## ##E_{ind} = E_{out} - E_{in}## ##E_{in} = \frac{E_{out}}{\varepsilon}## ##E_{ind} = E_{out} -...
  28. F

    Evaluate the outgoing radiation from an optical fiber on a surface

    The geometric configuration that I am adopting is the following, I hope you understand. The optical fiber is positioned relative to the bottom surface at a height ##a## and an angle ##\alpha## with respect to the y-axis in the yz-plane with x = 0. ##b## is the distance between the origin and...
  29. Philip Koeck

    I Surface charge of neutral solids

    Also referring to the post by @Kostik plus answers, I'm wondering about surface charges of neutral solids such as metals or carbon, for example. I only want to discuss large scale effects so that the solid can be treated as continuous. The atomic structure is averaged out. I also assume that...
  30. garryA

    Frequency selective surface radome

    So I was reading about frequency selective surface radome, basically this is the kind of cover over the antenna which allow a certain frequency wave to pass through and reflect wave at any other frequencies. What I don't understand is the reflection vs transmission coefficient chart. So as I...
  31. G

    Surface current on a spherical superconductor

    I need help with part b. My solution: Have I done it right?
  32. BiGyElLoWhAt

    3d plot of interference from 2 wave sources with 2d grid surface

    Desired output similar to image, but without the objects and with better wave interference: I tried plugging the following into wolfram (I specifically want the values to be adjustable): plot z= H*e^(-m*sqrt((x-a)^2+(y-b)^2))*sin(k*(x-a)+k*(y-b) -w*t) +...
  33. L

    Measured Surface Resistivity Much Higher than Theoretical Value (Why?)

    I recently conducted a physics lab to measure the surface resistivity of a conductive sheet of a paper with a carbon filler. The theoretical Rs is approx. 5,000 Ω/☐ for this paper and yet we have calculated two Rs values: Rs when Varying Length and holding Width = 10100 +/- 83.07 Ω/☐ Rs when...
  34. 1

    MCNP Surface Tallies: F1 & F2 on Infinite Cylinders & Planes

    Hi, I have a question concerning surface tallies like F1 and F2. You have to provide a surface for them. Since, surfaces are defined as infinite (infinitely long cylinders, infinitely extended planes) how can you write the surface tally of a cell? What are the actual tally surfaces for F1 anf...
  35. L

    Finding Charge Density on the Surface of a Slab

    Here's my attempt at a solution, but when I plug it in, it gives me a power ten error. I don't really understand what I'm doing wrong here. I think all my variables are in the correct units and it asks for my answer to be in μC/m2. Any help is much appreciated.
  36. C

    Need a surface mount seal for chemical cabinet door

    I want to build a mini chemical cabinet to try to eliminate odors in my garage as my wife thinks the car interior now smells. The chemical resistant rubber strip sealant is crazy expensive, but as the intended use will just be fumes with no actual chemical or fuel contact to the seals, can I use...
  37. C

    I How to calculate the Fermi surface nesting function

  38. C

    How does soap water membrane thickness affect surface tension?

    1.If the thickness of soap water surface decrease, whereas the concentration remain the same, how will the surface tension change? 2. If the membrane of soap water start to evaporate, its thickness become thinner and it’s concentration increase, How will the surface tension change? Thank you!
  39. G

    Chemistry How to compute specific surface energy for cubes of varying sizes?

    I got these values but I wanted to make sure I was doing it the correct way a) 0.548 J/g for system of 1 µm cubes b) 9.131 x 10^19 J/g for system of 1 nm cubes c) 273.890 J/g for system of 1 nm radius spheres
  40. M

    Electric field at surface of lead-208 nucleus

    For this problem, The solution is, However why is ## r = (208)^{1/3}(1.20 \times 10^{-15} m)## Many thanks!
  41. J

    I Surface Absorptance Without Radiant Emittance

    how can I go about finding the surface absorptance of a material if I'm not given the radiant emittance of the non- black body?
  42. chwala

    Find the surface area of the given solid

    My question is on how did they determine the limits of integration i.e ##2## and ##3## as highlighted? Thanks
  43. abdulbadii

    Force to smooth a 1 mm surface bump out of a steel of sheet

    Roughly, how much force does it take to make 1 mm surface bump of diameter 16 mm circle area out of 1 mm thick steel plate of far larger area (e.g. a muscled hand pounding it laid over the base with 16 mm dia. hole by M16 bolt medium is viable enough) ?
  44. Trysse

    B Oriented Surfaces & Surface Area: Investigating the Impact

    I usually think of a sphere as the set of all points ##P_x##, that have the identical distance r to some point ##C## which is the center of the sphere. I calculate the surface area ##A## of the sphere as $$A=4 \pi (C P_x)^2$$ However, what happens if I think of the distance between the points C...
  45. String theory guy

    Average force when a bouncy ball collides with surface

    What have mistakes/wrong assumption have I made in solving this question? I tried to solve the problem this way N.B. I assume that the j hat direction is up.
  46. String theory guy

    Doubt about solution -- Two masses connected by a rod moving on a surface

    The doubt is about this question. Which the answer is They say that all the forces are pulling forces? How is this the case? How would this setup even work? I don't think block 2 could pull the rod.
  47. R

    I Vacuum force factors (vacuum created by a "flow through" liquid)

    Greetings all, I'm new here and hope I'm asking this in the correct thread. So, the question is; where you have a vacuum created by a "flow through" liquid witin a large diameter container exerting suction force upon a smaller diameter input tube submerged in a liquid, does the surface area of...
  48. Addez123

    Calculate surface integral on sphere

    I'm supposed to do the surface integral on A by using spherical coordinates. $$A = (rsin\theta cos\phi, rsin\theta sin\phi, rcos\theta)/r^{3/2}$$ $$dS = h_{\theta}h_{\phi} d_{\theta}d_{\phi} = r^2sin\theta d_{\theta}d_{\phi}$$ Now I'm trying to do $$\iint A dS = (rsin\theta cos\phi, rsin\theta...
  49. gggnano

    I Is it possible to have "ideal surface" whose highest peak is ~1 nm?

    I mean you could buy a mirror or silicon wafer but they give say 0.5 nm or 5nm 'roughness' which I suspect is the mean average roughness but this doesn't rule out a high "bump" way above the mean average such that for example 1 million bumps of 1 nm and just one of 5 will result in...
  50. A

    B Speed of Point on Expanding Sphere

    Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?
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