Surface Definition and 1000 Threads

  1. A

    Normal Velocity Gradient Across a Surface: Proving a Result

    I have came across a problem where each point of a surface parallel to the x-y cartesian plane and having it's normal along the z axis is having velocity along the z direction ##v_z## and there exists a velocity gradient across the plane (e.g ##v_z(x,y)## , After time ##\delta t## it is written...
  2. fluidistic

    A What can the Fermi surface tell us about a material's properties?

    I would like to know every bit of information one can retrieve by looking at the Fermi surface of a material. Here's what I think is correct thus far: 1) The fact that the material has a Fermi surface already tells us a lot. The material could be a metal or something that resembles a metal...
  3. alexmahone

    Average electric field over a spherical surface

    I'm sure the average is going to be an integral, but \displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a} gives me a scalar, not a vector.
  4. A

    How to solve a surface double integral?

    Hi I´d like a suggestion about a surface double integral. If I have a sphere x^2+y^2+z^2=4 is on the top of a cardioid r=1-cosθ. The problem is when I solve the integral I got a inverse sine when the answer is a natural logarithm (ln)
  5. maistral

    I Fitting points z = f(x,y) to a quadratic surface

    Hi! I am aware that standard fitting numerical methods like Levenberg-Marquardt, Gauss-Newton, among others, are able to fit a dataset z = f(x,y) to a quadratic surface of the form z = Ax2 + Bxy + Cy2 + Dx + Ey + F, where A to F are the coefficients. Is there a simpler method that exists? I'm...
  6. E

    Show that a tilted free liquid surface undergoes shear stress

    i really can't understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow. i...
  7. DavidMasabo

    Need a force to accelerate an object on a frictionless surface

    Problem Statement: would you need a force to accelerate an object on a friction-less surface? How could one calculate the force? Relevant Equations: F=MA would you need a force to accelerate an object on a friction-less surface? How could one calculate the force?
  8. M

    Export a 3d surface movie with good quality

    Hi PF! I have a 3D surface that changes with time. I am trying to make a movie. The following is what I do, but the output is extremely low quality. Does anyone know how I can get the same quality that Mathematica uses for its images? mov[t_] := Show[ParametricPlot3D[{(2 + Cos[v]) Cos[U]...
  9. mishima

    Calculus of Variations, Isoperimetric, given surface area max volume

    My volume integral is... $$\pi\int y^2 dx$$ My surface area integral is... $$2\pi\int y \sqrt {1+x'^2} dy$$I'm fairly sure the variable of integration on my volume and surface area integrals has to be the same, is that right? But when I change the variable in the surface area integral to...
  10. M

    I Showing that B has no discontinuities at the surface

    Consider a magnetic dipole distribution in space having magnetization ##\mathbf{M}##. The potential at any point is given by: ##\displaystyle\psi=\dfrac{\mu_0}{4 \pi} \int_{V'} \dfrac{ \rho}{|\mathbf{r}-\mathbf{r'}|} dV' + \dfrac{\mu_0}{4 \pi} \oint_{S'}...
  11. M

    What will the electric field be at the surface?

    The electric field due to a dipole distribution in volume ##V'## can be viewed as electric field due to a volume charge distribution in ##V'## plus electric field due to a surface charge distribution in boundary of ##V'##. ##\displaystyle\mathbf{E}=\int_{V'} \dfrac{\rho...
  12. M

    Prove the dipole potential is differentiable everywhere except at the surface

    The dipole potential is given by: ##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV' +\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'## I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous) I know if...
  13. 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...
  14. 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...
  15. E

    Why Are Pulmonary Alveoli and Kidney Nephrons Spherical Instead of Tetrahedral?

    In a human body we have two relatively similar structures -pulmonary...
  16. 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...
  17. 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.
  18. 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...
  19. 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.
  20. 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...
  21. 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...
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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.
  27. 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...
  28. 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...
  29. 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...
  30. 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?
  31. 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...
  32. 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)...
  33. 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...
  34. 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...
  35. 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??
  36. 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...
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
Back
Top