Surface Definition and 1000 Threads

...and they can penetrate a bit in the surface, we could image the subsurface right? I do not see the problem... Help please!

If we apply an electrical insulating material on a bare conductor which carries 25 Kv AC Voltage. What would be the surface voltage observed on the insulating material? Is there any test/method by which surface voltage can be measured on the Insulating Material. The Insulating material has...

Hey everyone, I've been stuck on this one piece of HW for days and was hoping someone could help me. It reads: The surface area, A, of a sphere with radius R is given by A=4πR^2 Re-derive this formula and write down the 3 essential steps. This formula is usually derived from a double...

Is there a potential on the inner surface of a charged spherical shell? I know that there is no electric field on the inner surface, as shown by Gauss's Law, but that isn't enough information to say that the potential (V) there is zero since E = dV/dr, so V could be a nonzero constant. If...

Homework Statement Let S be the portion of the paraboloid ##z = 4 - x^2 - y^2 ## that lies above the plane ##z = 0## and let ##\vec F = < z-y, x+z, -e^{ xyz }cos y >##. Use Stoke's Theorem to find the surface integral ##\iint_S (\nabla × \vec F) ⋅ \vec n \,dS##. Homework Equations ##\iint_S...

Homework Statement Hi everybody! I'm currently training at surface integrals of vector fields, and I'd like to check if my results are correct AND if there is any shortcut possible in the method I use. I'm preparing for an exam, and I found that it takes me way too much time to solve it. I...

Homework Statement what will be Lagrange,s equation of motion for a particle confined to move on surface of sphere whose radius is expanding such that Homework Equations Euler-lagranges equation of motion d/dt(∂L/∂{dq/dt})-∂L/∂q=0 The Attempt at a Solution Z=(R+R0e^at)cosθ...

I'm given this problem to solve with the assumption as stated above. The answers need not be logical as long as the linkage mechanism can be simulated. I've attempted the question using Mercedes Mono Wiper mechanism but only manage to cover 41% given the width of the wiper. May I ask if there...

My teacher told me the other day that a semiconductor does not have a fermi surface. I didn't understand this remark. As I understand it the Fermi Surface is just the surface in k-space spanned by the highest occupied energy levels. Surely in a semiconductor you will also have some highest...

Homework Statement Hi, would like to get a feedback on my answer to this question, did I do it right? In part 2 of the question is there another way to calculate distance with friction? the question is: a disc is moving on icy surface has an initial speed of 12m/s 42m until it stops 1. what...

Homework Statement It is evaluating a surface integral. Homework Equations ∫s∫ f(x,y,z) dS = ∫R∫ f[x,y,g(x,y)]√(1+[gx(x,y)]2+[gy(x,y)]2) dA The Attempt at a Solution I set z=g(x) and found my partial derivatives to be gx=√x, and gy=0. I then inserted them back into the radical and came up...

Homework Statement Two pools A and B have exactly the same depth, but A has 10 times the surface area, both at the top and at the bottom. Find the ratio of the total pressure (a) at the top surface of A to that at the top surface of B (b)at the bottom of A to that at the bottom of B. Homework...

Dear all, I am looking for more information how specific activity \frac{Bq}{g} and surface activity \frac{Bq}{cm^2} is measured. This is done to determine whether the materials of interest can be treated as harmless and disposed as usual waste. I am interested how the experimental procedure...

Homework Statement It is known that the potencial is given as V = 80 ρ0.6 volts. Assuming free space conditions, find a) E, b) the volume charge density at ρ=0.5 m and c) the total charge lying withing the closed surface ρ=0.6, 0<z<1 Homework Equations E[/B]=-∇VThe Attempt at a Solution (this...

My book states that "irradiance at a point on the outer sphere is less than irradiance at a point on the inner sphere." The formula is simple, it's flux/area. So in case of a sphere its flux/4π*r^2. But my question is what exactly does this formula give? does it give the total flux that...

I am struggling to understand the relation between surface tension and surfactants. When surfactants are added to say water they may have charge and head groups which influence surface motion due to repulsion and their size. However often when people refer to surface tension they refer to a...

I am reading about angle-resovled-photoemission-spectroscopy (ARPES). It seems that it is a technique that gives the energy dispersion as a function of the momentum k. However in all talks about it, it seems to be a technique that gives us the fermi surface of the given structure. I don't...

Cauchy integral theorem states that the contour integration of a complex harmonic function along a closed simply connected path=0. What if this simply connected path is drawn over a Riemann surface of function like ##f(z)=\sqrt z##. Will that be possible in the first place? and will the...

Homework Statement when the normal vector n is oriented upward , why the dz/dx and dz/dy is negative ? shouldn't the k = positive , while the dz/dx and dz/dy is also positive? Homework EquationsThe Attempt at a Solution is the author wrong ? [/B]

Hey guys, I'm trying to prove to a friend something but I couldn't find a proof online. Imagine wind coming in from the side and hitting an upright cylinder. We're trying to find the force exerted, which then requires which kinda of cross section to use. I think the best way to calculate it is...

since magnetic field lines form closed loops , field inside Earth must be due geographic south will compass below Earth's surface point to geographic south?

Greetings All, I have a rather odd question which has been bothering me. If you have a perfectly round sphere sitting on a perfectly flat plane, what is the area of surface contact between the two? Is there an actual value, or is it something which can't be calculated. I'm assuming the diameter...

in part b , we can find mass by density x area ? is it because of the thin plate, so, the thickness of plate can be ignored?

I am a tenth grader, and a newbie to Advanced Calculus. While working out problems sets for Gauss's Law, I encountered the following Surface Integral: I couldn't attempt anything, having no knowledge over surface integration. So please help.

i am trying to figure out the relationship between diameter of a drop of liquid, its density and its shape. Can somebody explain to me the following two lines?

The other day I was wondering if as the universe is infinite and you can say that every single point in it is the centre of the universe, or that there is no centre for the same matter. Since you are not able to set up a centre in Earth's surface. Is then Earth's surface infinite? When you talk...

Hi, I'm trying to figure out the pressure that seawater would exert against a vertical surface (on average) over a large area but I am messing up somewhere. The height of the rectangle is 560 ft and the length is 20 miles, or 105,600 ft, giving an area of 2.12 mi². The weight of the water in...

Homework Statement True or not true:[/B] Equipotential surfaces of the magnetic field are no closed surfaces but extend to infinity Homework Equations - The Attempt at a Solution I think it is true, because they are perpendicular to the (closed) magnetic field lines, but I am not sure...

I am having a difficult time seeing the three dimensional surface formed from a plane of equation 2x + y + z = 2 strictly inside the first quadrant. On the 2 dimensional xy plane, the closed, simple, piece wise curve is C1 along the x-axis from x=0 to 1, C2 along the line y= 2-2x is between...

In the elementary proof of the slant surface area of a cone ##A=\pi r s##, where ##s## is the slant height, it is assumed that the net of a cone is a circular sector. In other words, if we cut the slant surface of a cone from its apex to its base along a straight line, the resulting surface can...

Are there any theorems that say something formal about the fact that any graph is drawable on a 2D surface, and can be mapped to a 2D array of pixels if the pixels are infinitely small?

Does there exist any 2D surface whose metric tensor is, ##\eta_{\mu\nu}= \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}##

As per the Gauss Law , Net Flux Electric Field through a closed Surface (Gaussian Surface) is zero if no charge is enclosed. As per the definition of the Electrical Flux = Electrical Field Intensity dot product Area Vector i.e. Closed Integral of E.S If Electrical Flux is zero then as per the...

Why does Gauss' law hold for any closed surface? and can you show this mathematically. Many thanks :)

Hey there, I'm struggling in finding the useful equations to determine some conformability parameters for a finite elastic material (EPDM) compressed on a rigid slightly wavy surface. I would like to optimize the thickness of the elastic material in terms of indentation depth and thus contact...

Homework Statement I want to understand why in noncicular members in torsion book tells me that surface of a member is free and so no shearing stresses there. This is from wikipedia for shafts: Note that the highest shear stress occurs on the surface of the shaft, where the radius is...

Homework Statement The block was given an initial velocity up the surface with an angle of 45 degrees to the ground. Calculate the ##\frac{t_1}{t_2}## with ##t_1## being the time it took to get to the highest point up the hill and ##t_2## the time it took to get down. In both cases the...

Homework Statement Homework EquationsThe Attempt at a Solution Pressure inside bubble = 2T/R Buoyant force on bubble = ##\frac{4}{3} \pi R^3 ρ_w g ## But I do not understand how surface tension is exerting force on the bubble .Also I do not understand the direction of surface tension force...

Hi Guys... I have a small doubt regarding surface tension. When calculating the relation between Pressure Difference inside and outside a Droplet and Surface Tension, we multiply Pressure Difference with Cross Sectional Area of the Droplet and equate it to the Surface tension force. My doubt is...

I know that Killing horizon is the hypersurface on which timelike Killing vector field becomes null. Beyond that surface Killing vector field becomes spacelike. But Stationary Limit Surface has also such a property. I wonder, if they are the same thing, if so, why is there different names for...

Homework Statement A ray of light falls on the surface AC of a prism with a straight angle and with two sides equal. For which incidence angle the ray won't come out of the surface AB. The index of refraction for the prism is n=2. Homework Equations sina/sinb=n2/n1 The Attempt at a Solution...

Let's say we have r=R( theta, phi, t) on the surface of the particle and need to find the normal vector in Spherical Coordinate system. We know that, the unit vector =grad(r-R( theta, phi, t)) / |grad((r-R( theta, phi, t))| where grad is Spherical gradient operator in term of e_r, e_\theta...

Homework Statement A slab of material has parallel faces. One coincides with the xy plane (z = 0), while the other is given by z = zt . The material has a nonuniform polarization P = P(1 + αz)zˆ where P and α are constants. Fin the volume and surface densities of bound charges[/B] The Attempt...

Homework Statement I'm trying to figure out the surface area on a 5 sided shape where the sides can all be modeled by "lunes". The shape will end up looking like a banana peel. We are modeling the sides of the shape as lunes with varying angles on a sphere of radius 3 inches. I'm trying to...

Hello. Recently, I have read the article about plasma surface treatment. The article says contact of the plasma to the surface of the sample increases surface energy by transferring plasma energy to the surface. Then it is suddenly saying that wettability of some industrial ink or paints on...

What determines the surface temperature inside a pot of boiling water, right over the heat source? Can it go much over boiling temp if the water's just gently boiling?

Having trouble to understand a classical example of surface tension: Two balloons are connected to each other with a valve. If the surface tension of the two balloons is the same but one balloon is bigger than the other, when the valve is lifted open so the air in the two balloons is now...

Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same) Flux is the dot product of electric field and surface area, so wouldn't it change if surface area is changed?

I'm told that graph of the surface $g(x,y,z) = x^2+y^2+4z^2 = 1$ looks like: Is that correct? And if so, I've the following question. When considering the slices the graph of $g(x,y, z)$ is a circle in the $xy$ plane and an ellipse in the $xz$ plane and $zy$ plane. The circle is bigger than...

Hi Community, I have this tutorial question. When I look at the first question (a) I think it is FALSE as the surface area would not increase at the same rate as the radius. For the second question I am not sure if I am interpreting it correctly. If r=\sqrt{\frac{Ct}{4\varPi}+2} where Ct is...