Surface Definition and 1000 Threads

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.

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?

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...

Hi, if I have a block of metal with a quarter circle curve cut out of it, and a metal roller of matching radius that contacts this curved piece, what are some ways I could go about measuring the friction between these two surfaces? The roller is fixed and the block is pushed into it with a...

Homework Statement Use a line integral to find the area of the surface that extends upward from the semicircle ##y=\sqrt{9-x^2}## in the ##xy##-plane to the surface ##z=3x^4y## Homework Equations Parametric Equation for Circle: ## x = rcos(t) ## ## y = rsin(t) ## Line Integral: ## \int_c...

Suppose a cylindrical rod is given a push such that it rolls without slipping on a horizontal plane. Am I right to say that rolling friction is only required at the start when the push is applied to initiate the rolling motion? Once the push is removed, the only forces acting on the rod are its...

Homework Statement A body moves down along an inclined plane from A(top) to B(bottom), and then moves on the floor in continuation to some point C. (All surfaces are frictionless) After reaching B, body is having some acceleration. But while moving from B to C, a) will it keep on...

I think its a defination to have infinite longitudnal lines , if line are not perpendicular than the infinite point will not add up to give the circumferance of equator, please help

Hello Forum, In the case of an ideal, thin lens (free from any aberration), it does not matter which face of the lens is facing the object. The results will be identical. What if the lens was an ideal (no aberration) thick less with the H planes, etc...? Would it matter which lens surface is...

Homework Statement Problem is in image uploaded Homework Equations n/a The Attempt at a Solution x = u, y = v and z = 1 - u - v ∂r/∂u × ∂r/∂v = i + j + k F dot N = u^2 + 3v^2 ∫∫(u^2 + 3v^2 )dudv My problem is I'm not sure what I should take as the limits? Should I flip around the order of...

Homework Statement Two blocks, A and B , are being pushed on a frictionless surface by a froce of 30 N to the right, .Block A has a mass of 2.0kg, Block B, being pushed by Block A is 4.0kg. Calculate the magnitude of the force that block B exerts on Block A. Homework Equations f=ma The...

Hello, This problem is about cooper pair formation and what happens with the calculations if there is an attractive potential between electrons but it is not in the presence of a filled fermi surface. 1. Homework Statement Two electrons just above the filled Fermi Surface of a material can...

Homework Statement Sorry- I've figured it out, but I am afraid I don't know how to delete the thread. Thank you though :) Homework Equations Below The Attempt at a Solution Photo below- I promise its coming! I've started by using cylindrical coordinates, but I wasn't sure if spherical...

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...

Homework Statement a) A charge q is released a distance d above a grounded infinite conducting plane. It's non relativistic velocity is v. Find the induced surface current density on the plane. b) Show that the above current density produces a vanishing magnetic force on the charge. Homework...

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...

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...

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...

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...