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.
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...
Q:- Describe equipotential surface due to a uniform grid consisting of long equally spaced parallel charged wires in a plane.
The answer given in my textbook is - Equipotential surface have shape which changes periodically. At far off distances it becomes parallel to the plane.
Why the...
"A metallic wall cannot, however, support an electric field parallel to the surface, since charges can always flow in such a way as to neutralize the electric field."
This is from a textbook and I'm not quite sure what this means.
The context is the process of calculating Rayleigh and Jeans...
Hello all,
- first of all sorry for my bad english, it's not my mother tong.
- I write here because I want to understand that are the surface waves and how can we demonstrate their existence ? Do you have a PDF file which speak about this ?
- For volumic waves I have seen a mathematical...
I was asked to explain how different factors affect surface tension. I can understand how temperature plays a role.
1) Contamination:
Increase in contamination decreases surface tension. I tried thinking about it.I thought maybe the particles that contaminate the fluid get in the way and...
Homework Statement
What should be the pressure inside a small air bubble of 0.1,, radius,situated just below the surface? st of water=7.2 *10-2 and atmospheric pressure=1.013*105.
Homework EquationsThe Attempt at a Solution
I am of the understanding that the pressure inside the...
Hi, i would like to know how to do this question for fluid mechanics. Sorry as I am new i didnt know how to upload images so i just uploaded the image in justpaste, here is the link http://justpaste.it/pz7r
How, if at all, would differential geometry differ between the opposite "sides" of the surface in question. Simplest example: suppose you look at vectors etc on the outside of a sphere as opposed to the inside. Or a flat plane? Wouldn't one of the coordinates be essentially a mirror while...
Homework Statement
Hi, as a part of my lab report I have to conduct this experiment : Fill a pot with tap water and boil it, determine then how much of the energy that the kitchen surface produced, actually went to the water itself. Consider the water having an initial temperature of 10 °C. In...
There is a distorted surface and the source of the flux is inside the cube
I have read that flux through it would be q/2ε0 I want to know Why?It is not my homework problem and I think it does not involve any calculation that's why I did not post it in homework section .There should be some...
Joos asserts on page 31 https://books.google.com/books?id=btrCAgAAQBAJ&lpg=PP1&pg=PA31#v=onepage&q&f=false that
$$\nabla \times \mathfrak{v} = \lim_{\Delta \tau \to 0} \frac{1}{\Delta \tau }\oint d\mathfrak{S}\times \mathfrak{v}$$
I tried to demonstrate this, and neglected to place the surface...
Homework Statement
A large sphere exists in space, which has a mass of 1 * 10^28 kg
The sphere has a radius of 100,000 km
What will be its gravitational pull (aka: "relative gravity") on its surface in terms of gs (1 "g" being equal to the gravitational pull of the Earth which is 9.807 m/s^2)...
The HadCRUT4 global surface temperature anomalies in tabular form include confidence intervals.
The GISS surface temperature data is available in tabular text form here http://data.giss.nasa.gov/gistemp/tabledata_v3/GLB.Ts+dSST.txt
- but it doesn't include any confidence intervals.
Can...
What is the "plane of symmetry", "zero velocity wall" and "free surface" terms which I have seen in Polyflow? It says in Vnormal=Fs=0 for plane of symmetry and Vnormal= Vs= 0 for zero velocity Wall. Now I get when Vs=Vn=0 it means that the wall isn't moving and it's in a static state but didnt...
Homework Statement
How do I find the surface area of a sphere (r=15) with integrals.
Homework Equations
Surface area for cylinder and sphere A=4*pi*r2.
The Attempt at a Solution
I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite...
The following is my interpretation of the development of the divergence of a vector field given by Joos:
$$dy dz dv_x=dy dz\left(v_x(dx)-v_x(0)\right)=dy dz\left(v_x(0)+dx\frac{\partial v_x}{\partial x}(0)- v_x(0)\right)$$
$$=dy dz dx\frac{\partial v_x}{\partial x}(0)=d\tau \frac{\partial...
Homework Statement
Compute the average number of molecular hits, per unit time, experienced by a square inch of surface exposed to air, under normal conditions. Assume air is a mixture composed of 80% N2, 20% O2, both of which are assumed to be ideal gases. You will have to perform angular...
Homework Statement
The plane with surface charge sigma lies in x-z plane at y=0, parallel to it at y=a there is a grounded plane. What is the field just above the bottom plane, find the potential between the planes
Homework Equations
discontinuity E=sigma/epsilon, V=Qd/Aepsilon take the...
We are currently trying to measure pH levels on the (wet) surface of metals as part of a study about corrosion.
The surface may have a non-conductive protective layer.
- is it feasible to measure pH on a planar surface (dry or wet)? Which kind of sensor probe can be used for this task?
-...
I was just looking through a few different solutions in Griffiths EM and I must have not realized it, but do bound and free charges both contribute to the overall electric field?
For example: when dealing with a capacitor with a dielectric between it, one of the solutions wants to find the...
Hello guys,
Consider a partially filled tank with water where the acoustic field can be described by the Helmholtz equation.
The boundary condition at the water surface would be \frac{∂p}{∂\vec{n}} = -j\rho_0\omega\frac{p}{Z}
where Z is the impedance of the water surface.
What would be...
Hello guys!
I have to model the acouctic field within partially filled cavities.
So consider a rectangular or cylindrical cavity that is partially filled with water. I would like to model the water layer as a sound absorbing wall by prescribing it as a surface impedance boundary condition...
Homework Statement
New to physics forum, so please forgive me if I am posting this in the wrong place, but it seems to me that this is a homework-type or basic physics question. Here it is: You have a perfect cube with substantial mass sitting on a flat frictionless surface. The surface plane...
Homework Statement A cylindrical container of water with a radius of 6.0 cm is placed on a phonograph turntable so that its outer edge just touches the outer edge of the turntable. The radius of the turntable is 14.5 cm, and the turntable rotates at 33 and a 1/3 revolutions per minute. How much...
Homework Statement
A child stands on frictionless ice and throws a snowball. Estimate the recoil velocity of the child.
Homework Equations
m1v1i + m2v2i =m1v1 +m2v2f
1/2mv21i + 1/2 mv22i = 1/2 mv21f + 1/2mv22f
The Attempt at a Solution
After choosing estimates for weight of snowball, speed of...
Homework Statement
Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...
Homework Statement
A 3 m long gate of weight 4 kN per unit width is hinged at O and sits at an angle θ as a function of water height h above the hinge. (A) Using a y-axis measured up from the hinge, derive a general relation between h and θ, with all other variables evaluated in the relation...
I am trying to figure out the flux surface average of a 3D perturbation in a tokamak. For example what is the flux surface average of cos(m*theta+n*phi) at a given flux surface. (Theta and phi being poloidal and toroidal angles respectively?
Hi everyone.
I'm looking for some help from someone expert in optics to create an inteferometry based setup to map the surface of a small object. This is for a small lab project so I'm not looking for a really complex setup, I just need something simple that can be built in a short amount of...
Homework Statement
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Homework Equations
##\vec{E}##=##\frac{∂V}{∂r}##
The Attempt at a Solution
I have provided both problem and solution(almost)but the problem is I did not understand the solution.First of all
I did not understand the question what we are told to determine?
I locate the...
Homework Statement
\vec J_b = 3s \hat z
\int \vec J_b \, d\vec a
I need to solve this integral in cylindrical coordinates. It's the bound current of an infinite cylinder, with everything done in cylindrical coordinates and s is the radius of the cylinder. The answer should end up with a phi...
Hi,
I've been doing reading on Halbach Arrays moving over surfaces and generating repulsive forces. From my understanding, the moving magnet induces a circular electric current in the metal track, which gives rise to a magnetic field.
However, I'm having trouble understanding why this field...
We just started going over line integrals in calculus, and have been told that the integral over any closed surface is 0. What I don't get is then why can we do the line integral of a circle to get 2##\pi##r? Since a circle is a closed surface, shouldn't the line integral then be 0?
I have recently had a series of lectures on X-ray physics. I have been quite confused by the concept of effective dose and entrance surface dose.
I have been told that entrance surface dose varies proportionally to kV squared. I have also been told that as kV increases, effective dose...
Hi,
I am trying to get some information about why Matt black surfaces are such good emitters and shiny surfaces are not. When you try and look this up there really isn't much so I have tried to string what I have found together.
Shiny metal surfaces have free electrons which cancel the...
1. Introduction
Pressure of a fluid exerts thrust on each part of a surface with which the fluid made contact. Each forces distributed over the area have a resultant magnitude and direction that is very crucial. For a horizontal surface, the pressure does not vary over the plane. Thus, the...
Homework Statement
Calculate the integral ##\oint_C \vec F \cdot d\vec S##, where ##C## is the closed curve constructed by the intersection of the surfaces ##z = \frac{x^2+y^2}{4a}## and ##x^2+y^2+z^2=9a^2##, and ##\vec F## is the field ##\vec F = F_0\left( \frac{a}{\rho}+\frac{\rho^2}{a^2}...
I'm trying to deduce the differential equation for temperature for a triangular fin:
I know that for a rectangular fin, such as:
I can do:
Energy entering the left:
q_x= -kA\frac{dT(x)}{dx}
Energy leaving the right:
q_{x+dx} = -kA\frac{dT(x)}{dx} - kA\frac{d² T(x)}{dx²}dx
Energy lost by...
Hello !
Homework Statement
In an exercise we consider two surfaces
given by
f1=(x,y,f(x,y)) defined in a domain D
And
f2=f1 in D'
And a line d with two parametrizations
d1=(f(y,z),y,z)
d2=(x,f(x,z),z)
They ask to find the principal curvatures of S1 U S2 U d
Homework EquationsThe Attempt at a...
I'm confused what the difference between the two are...I thought surface brightness was luminosity, but apparently it's not: L=Surface brightess x Area...But I came across a similar equation that seems to assume surface brightness is the same as apparent brightness. Please help!
Edit: Also, why...
Can anybody explain under what conditions does this happens?
Why does the light beam travel on the curved surface? How does this happen? Isn't light suppose to travel in straight line?
A Cauchy surface is a 3d spacelike slice of spacetime.
Could you read the definition (17) p18
the author says that "one can proove that ##\sigma## does not depend on the choice of the Cauchy surface because the functions obey the law of motion."
Could you elaborate?
Thanks
Could anyone add "h"...
Homework Statement
Find the point on the surface z2 = xy + y + 3 which is closest to the point (1,2,0)Homework EquationsThe Attempt at a Solution
Can someone check my work?
Hey guys!
What would be the gravitational effect of Earth on it's surface, if somehow the density of mass was uniform and equal to 2/5 of the real value? Assuming that the size e shape os the planet doesn't change.
Hi,
So for a piece of maths coursework I am thinking of trying to calculate the surface area of an atom or molecule. I do not know whether it would be viable because there isn't a clear boundary for an atom/molecule due to the electron clouds. However I wanted to know if I could do something...
Homework Statement
A 3.0 kg block is held against a spring with a force constant of 125 N/m. The spring is compressed by 12 cm. The ice is released across a horizontal plank with a coefficient of friction of 0.1
A) Calculate the velocity of the block just as it leaves the spring. Assume the...
Homework Statement
A 100N box is initially at rest on a rough horizontal surface. The coefficient of static friction between the box and the surface is 0.6 and the coefficient of kinetic friction is 0.4. A constant 35N force is aplied to the box horizontally.
Identify from choices (a) - (e)...
Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution...
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...
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