Surfaces Definition and 425 Threads

Hey, Completing AP Problems, I ran into a puzzling answer. Basically, there was a conducting sphere with charge Q on it and radius R1, and then around it two hollow hemispheres were placed (forming a spherical capacitor) which had no charge, with Radius R2 at the inner edge and R3 at the...

Homework Statement Find the volume bounded by the following surfaces: z = 2(x^{2}+y^{2}) z = 18 y = \frac{1}{\sqrt{x}} y = -\frac{1}{\sqrt{x}} x\geq0 The Attempt at a Solution I have no Idea how to attempt it! I mean, I will, somehow. But want to know a straight-forward way. Would...

Homework Statement Prove that the curve \vec{r}(t) = <cost,sint/sqrt(2), sint/sqrt(2)> is at the intersection of a sphere and two elliptic cylinders. Reparametrize the curve with respect to arc length measured from (0, 1/sqrt(2), 1/sqrt(2)) in the direction of increasing t. Homework Equations...

Hello all. I'm trying to figure out how to determine the correct sign of paths and surfaces defined for calculating quantities in electromagnetic problems. For example, say there's a wire in the shape of a rectangular prism along the z-axis with some current density, \vec{J} . Then the...

Firstly, I'm a bit confused about EM wave propagation. Take the picture you see everywhere illustrating the perpendicularity of E and B in a traveling EM wave (like this http://web.onetel.net.uk/~gdsexyboy/em_wave.jpg) -- does that actually illustrate the magnitudes of E and B at a particular...

Just working on some practice problems. I missed a couple classes due to sickness and just need some extra help. If you could walk me through how to do these types of problems that would be amazing. Homework Statement Evaluate the volume of the solid bounded by the surfaces (x2 + y2)1/2 =...

I'm trying to show that the electric field for an infinitely large plate is E = \frac{\sigma}{2\epsilon_o} I was wondering why you can only use a cylindrical gaussian surface and not a cube? Thanks

Gaussian surfaces...need help...can someone help walk me through this problem?? A solid insulating sphere of radius 5 cm carries a net positive charge of 2 μC, uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius 10 cm and...

Homework Statement Find the volume of the solid enclosed by the parabolic cylinder y=10 - a2x2 and the planes z=y and z=2-y, where a > 0 is a constant.Homework Equations I have graphed the 3 surfaces on Maple to visualize the solid enclosed by these surfaces but the problem is there is no...

Friction is necessary to make motion rolling but if the body is already in rolling motion on rough surface without slipping then, is friction necessary to continue the rolling motion ?

Homework Statement Two infinitely long wires running parallel to the x-axis carry uniform charge densities \lambda and - \lambda. a.) Find the potential at any point (x, y, z) using the origin as your reference. b.) Show the equipotential surfaces are circular cylinders, and locate the...

I have a couple of questions, but probably only need one worked out to figure out the rest. 1. Find a function f(x,y,z) whose level surface f=8 is the graph of the function 3x+4y => I know that a level surface for f(x,y,z) is the solution to f(x,y,z)=k. However, now I'm stuck. I know how...

A curve in space is specied by the one parameter set of vectors x(t). Also given is a surface in space parameterised by x(u, v): x(t)= <2+t, -t, 1+3t2> x(u,v)=(u2 - v + u, u+5, v-2> A) Show that the curve intersects the surface in exactly two points. Show that xi = <4 - \frac{\sqrt{46}}{2}...

Hey I have to do a project in which I am going to roll a soccer ball across different surfaces such as turf, grass, concrete, etc... and calculate the force of friction of each of these surfaces. I believe that i need to find the Initial force of the ball, then the final and subtract to find the...

Homework Statement A vector field h is described in cylindrical polar coordinates by ( h equation attached ) where i, j, and k are the unit vectors along the Cartesian axes and (er) is the unit vector (x/r) i+(y/r) j Calculate (1) by surface integral h through the closed surface...

Express f(x,y,z) = yz in terms of u and v and evaluate \int\int_S f(x,y,z)dS This is supposed to be simple but I really don't know how to do this. I rewrote f(x,y,z) = yz as x = g(y,z) so then \Phi(y,z) = (y,z, x) Tx = (0,0,1) and Ty=(1,0,0) and their corss product, n, is <0,0,-1> Am...

Homework Statement Find the area of the surface that is the boundary of the region enclosed by the surfaces x^{2}+y^{2}=9 and y+z=5 and z=0 Homework Equations A(S)=\int\int_{D}\left|r_{u}\times r_{v}\right| \; dA The Attempt at a Solution I am really confused as to what he...

Are area vectors of oriented surfaces always perpendicular to the surface?

Homework Statement \rho = sin\theta * sin\phi Homework Equations I know that \rho^{2} = x^{2} + y^{2}+z^{2} The Attempt at a Solution I tried converting it to cartesian coordinates but I can't seem to get a workable answer that way. I know that the answer is the sphere with radius...

A little clarification is required for the following techniqueTHE TECHNIQUE Given a surface z = f(x,y), and some point Q in R3 (not on the surface) The point P on the surface for which the distance from P(x, y, f(x,y)) to Q is the shortest distance from the surface to Q (i.e. vector PQ has...

Hello everyone - I'm a third year student at Cambridge university, and I've recently started taking a course on Riemann surfaces along with a number of other pure courses this year. The problem is, the lecturer of the course is of a rather sub-par standard - whilst I don't doubt he's probably...

does friction in any way increase when the surfaces get very smooth ...? a teacher told us that it can increase due to electromagnetism...is it true...i searched the net but couldn't get any useful info...

Homework Statement The surfaces S1 : z = x2 + y2 and S2 : x2 + y2 = 2x + 2y intersect at a curve gamma . Find a tangent vector to at the point (0, 2, 4). Homework Equations i thought about finding gradients of the two functions and plug in the given point in the gradients and cross...

Last night in a lecture my professor explained that some partial differential equations are used to observe events on minimal surface (e.g. membranes). A former advisor, someone that studied differential geometry, gave a brief summary of minimal surfaces but in a diffy G perspective. 1.)...

When light approaches and enters a material, why does all the reflection happen at the surfaces? I mean, light is coming at say, some crystalline solid. It hits the first plane of atoms and some is reflected. Some goes into the crystal and passes through the 2nd, 3rd, 4th,..., (n-1)th plane of...

I was solving this question in rotational mechanics (not asking for help). The author then goes to solve this using energy conservation, equating the final kinetic and rotational energy to the initial potential energy. Now, he obviously assumed the object rolled on the surface, which, if...

Hi there, I am learning about quadric surfaces in my second year multivariable calculus course. I would like to know how most people would identify (find the name of) a quadric surface if they had the equation. We only need to know 6 different quadric surfaces, so should I ... (a)...

Homework Statement See first figure attached Homework Equations The Attempt at a Solution I was able to sketch the two curves individually to get an idea of what I'm looking at, but I still can't really visualize how the two curves would intersect each other in the first octant...

Homework Statement Find the equations of the normal lines to the surfaces at the given points. z=(3/4)x^2+3y^2 @ pt. (2,1) 2. The attempt at a solution I have already found the equation of the tangent plane and know it is correct. Tangent plane => (z-6)=3(x-2)+6(y-1) Now, I am confused...

In Marion & Thorton problem 1.29 asks to find the angle between two surfaces (x^2 +y^2 + z^2)^2 = 9 and x + y + z^2 = 1 at a point. The solution takes the gradient of (x^2 +y^2 + z^2)^2 - 9 and x + y + z^2 - 1, and using the dot product between the two vectors at that point gets the angle...

Homework Statement Find a vector parameterization of the intersection of the surfaces x2+y4+2z3=6 and x=y2 in R3. The Attempt at a Solution I let x=t. Then y3=t I solved the first equation for z in terms of x z = cube root ((t2+(t(cube rt(t)) - 6)/-2) I know this is wrong...

:bugeye:Hi All... I am really confused about the mechanism of loss of energy when an EM wave hits a metal surface. I always thought the reflection was due to the motion of the electrons in the metal (due to the electric field of the wave). Which suggests that resistive losses would come...

I am wondering if the following mod 2 cohomology class which can be defined on any compact surface, has any geometric meaning or is important in any way. triangulate the surface then take the first barycentric subdivision. This is a new triangulation. Define a 1 - cochain on this new...

Why of two floors made of the same material, the polished one is (at least feels) colder than the rough one. Just compare two concrete floors, one polished and one unpolished. Thanks

Homework Statement See figure Homework Equations The Attempt at a Solution Just to give the readers some background on my current situation, Recently I've been doing some independent study on some of the material that will be covered in upcoming math analysis course I'm...

Is a null hyperplane a Cauchy surface in Minkowski spacetime? What in case of other spacetimes?

Homework Statement Sketch the equipotential surfaces which result from the following charge configurations: (a) a point charge (b) a spherically symmetric charge distribution (c) a very large, plane, uniformly-charged sheet (d) a long, uniformly-charged cylinder (e) an electric dipole...

Dear all, I do really need your help. I'd like to find the volume contained between a sphere (x^2+y^2+z^2=r^2) , plane1 (ax+by+cz+d=0), and plane2 (z-h=0). Would you please check what I've done till now? From the sphere and plane1 equations I got: x1=sqrt*(r^2-y^2-z^2) x2=d/a-(b/a)y-(c/a)z...

Please explain to me in detail why a gaussian surface within a conductor has an electric field of zero? thanks.

Hello, I just need to know whether or not surfaces with zero size in the third dimension, 6x8x0, is considered two-dimensional. The surface is there all the time. It has a location in the third dimension, so wouldn't it be a 3D object? I am not sure whether I should call a flat surface (as...

How do we define the dimension of a surface? I know surfaces are 2-D but I don't really get where that comes from.

Hi! I need to know how to work with quadric surfaces to draw a 3D structures in a code. However I have no idea how to do this. I can't find any place in the internet where they explain quadric surfaces for newbies... Can someone point me in the right direction, please? I didn't post this...

Hi, I am trying to solve a basic question from a Fluid dynamics textbook. Could you help me with the answer? The question is as follows: A closed vessel full of water is rotating with constant angular velocity \Omega about a horizontal axis. Show that the surfaces of equal pressure are...

Hi The dispersion of Bogolyubov quasiparticles in a d-wave superconductor is E(\mathbf k) = \pm \sqrt{\varepsilon (\mathbf k)^2+\Delta (\mathbf k)^2}, where ε(k) is the normal-state dispersion and ∆(k) is the gap dispersion. My question is: The Fermi surface (FS) of the normal...

Im trying to check my answers to a problem, and in the past I've used a 3d grapher to graph functions like f(x,y) = whatever. but now i need to find a tangent plane to a surface at a point. the surface is: x2y+y2z-z2x=1but i don't know how to go about graphing something expressed that...

So the question is as titled i) f=(x^2 +y^2 +z^2) ^1/2 if I can figure out the method I can solve the other equations but I'm not really sure where to start I know that a function f(x,y,z) of a level surface well be constant so do I just find del f ?

Hi, everyone: How do we show that 2 planar surfaces in R^4 intersect at points (possibly empty sets of points, but not in lines, etc.). I am curious to see how we justify the Poincare dual of the intersection form in cohomology being modular, i.e., integer-valued...

Homework Statement Attached question Homework Equations The Attempt at a Solution I tried rearranging S1 for Z then using Maple to plot it, which gave me a cone extending from the point z=1. For S2, would I have to plot it twice? once for <1 and once for =1? I have no...

Dear all, In Density Functional Theory (DFT) the Kohn-Sham eigenvalues are used to construct the band structure and the density of states (DOS). For a 3D extended system the eigenvalues are determined up to a constant since there is no absolute energy reference, while for a 2D extended...