Surfaces Definition and 425 Threads

Homework Statement Consider the equation below. x^2 = 3y^2 + 5z^2 Reduce the equation to one of the standard forms. I believe its surface is a cone, but I'm not sure how to get it into the form z^2/c^2 = x^2/a^2 + y^2/b^2 thanks!

Find the angle between the surfaces defined by r^2= 9 and x + y + z^2= 1 at the point (2,-2,1)? --- I know this should be extremely simple but it is blowing my mind for some reason. Any help would be greatly appreciated.

I'm faced with a problem where I need to determine the intersecting point of three different surfaces. Normally I would do this by using the incredibly painful method of Lagrange multipliers. However, this computation needs to be done relatively quickly and I can afford some error, in the...

Hi, I posted this under General Physics but I thought I should post this under the math section too in case there are mathematicians who do not read posts under General Physics. I read some papers online about Calabi-Yau surfaces but I have some basic questions about them if you can answer...

Hi everyone, hope this is the right place to put this :) I have just finished "Theory of Functions" Vol. 1 & 2 by Konrad Knopp. I'd like to continue with a book that picks up where the second volume it left off. (Especially would be nice is a more "modern" book) The second volume is about...

How would you find voltage difference between two surfaces? If you are given a capacitor with an internal electric field that varies E. You also have the charge (sigma) and the radius of the inner surface r1 and the radius of the outer surface r2.

[SOLVED] potential of two surfaces coming together lets say we have two water droplets(assume them to be spherical shape) with a each having charge q and each has the potential at its surface as kq/r.What is the potential if the two water droplets combine? I thought tht the radius and charge...

I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment. A: Well, the statement of the theorem is clear, that Every closed Surface is homeomorphic to: 1) a sphere, 2) the connected sum of g tori 3) or the connected sum of g...

Homework Statement Hi all. Please take a look at the following problem: Evaluate the surface integral \int{F \cdotp d\vec{S}} for the following vector field: F(x;y;z) = xyi + yzj + zxk, where i, j and k are unit vectors. S is the part of the paraboloid z = 4-x^2-y^2 that lies above the square...

Dear all, Two hollow conducting spheres have a common center O. The dimensions of the spheres are as shown (attached above). A charge of −200 nC is placed on the inner conductor and a charge of +80 nC is placed on the outer conductor. The inner and outer surfaces of the spheres are...

I have two questions about electric field and equipotential surface. Here is first one: For an arrangement of two point charges, --Is it possible to find two points (neither at infinity) where E = 0 ? Secondly, --Is it possible for two or more different equipotential surfaces to intersect?

Rough (not smooth) surfaces often appear to be darker in sunlight when they are covered by water.How can we explain this physical phenomen?

[SOLVED] Parametric equation of the intersection between surfaces Homework Statement Given the following surfaces: S: z = x^2 + y^2 T: z = 1 - y^2 Find a parametric equation of the curve representing the intersection of S and T. Homework Equations N/A The Attempt at a Solution The...

[SOLVED] Equipotential surfaces Homework Statement http://personalpages.tds.net/~locowise/test/equipot1.jpg Fig. 1 -- Some equipotential surfaces In the figure above, you see a set of equipotentials representing an electric field in the region and some labeled points (A..G). What is...

[SOLVED] Equipotential Surfaces Question If the radius of the equipotential surface of point charge is 14.3 m at a potential of 2.20 kV, what is the magnitude of the point charge creating the potential? have V = [1/4πεo] [q/r] Given that, V = 2.20kV = 2200V r = 14.3m...

the question is.. Find the areas of the surfaces generated by revolvin the curves about the indicated axes. x = (1/3)y^(3/2) - y^(1/2), 1≦y≦3; revolved about y-axis so i use the general formula "S = Integral 2π (radius)(dS)" and the radiu in this case is x which is (1/3)y^(3/2) -...

Homework Statement Figure 24-34 shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 2.62 x 10-22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between...

z=x^2+y^2 and x^2+y^2+z^2=2...I need to find the intersection of these two surfaces. Would I just substitute z=x^2+y^2 into the equation of the sphere to find the curve of intersection? But when I do that I get an equation with fourth powers and I don't know what kind of curve that makes.

1) http://www.geocities.com/asdfasdf23135/advcal13.JPG Let F1 = x^2 - y^2 + z^2 -1 = 0 F2 = xy + xz - 2 = 0 F3 = xyz - x^2 - 6y + 6 = 0 My thought is to compute the gradients, grad F1 and grad F2. Then by taking their cross product, I can get a tangent vector v for the curve. Now, I can feel...

Homework Statement Can someone please define contour map for equipotential surfaces in really simple terms. I understand that the potential diff is from the neg side I don't understand what it means when the lines are closer together? I thought the lines are just divisions of the voltage...

A capacitor C is made from large disks with a very large R and the gap between the plates s is very small (s<<R). The connections to the plates are made "inside" the capacitor (on the inner surfaces) at the center of the plates. The capacitor is hooked up to a battery and switch. The circuit...

Consider the ellipse: (\frac{x}{2})^2 + y^2 = 1 We rotate this ellipse about the x-axis to form a surface known as ellipsoid. Determine the area of this surface. Start off by solving for y. y = \sqrt{1-\frac{x^2}{4}} Then find the derivative. y' =...

Homework Statement http://img526.imageshack.us/img526/4890/asdny3.jpg *Length of each side of the square is 3. *Length of DP = Length of BQ = Length of GR = 1 Calculate \theta, the angle that is made between the surface of PQR and the surface of CGHD Homework Equations No...

I'm looking for a 3D-graphing-freeware that's takes x, y, z variables (axis dependence) because I want to see how the different coefficients and constants change the graph. I've tried two open-source programs thus far and none of the accepts the equation for ellipsoids.

Hi everyone, I'm pretty new to Physics Forums but it seems like a fairly friendly community. :) Homework Statement Determine the equation of the surface formed when the line x=3y is rotated about the x-axis. Homework Equations x=3y is the given line.The Attempt at a Solution First I...

hi how can the following be proved using integral methods: a) prove surface area of sphere, radius a, is 4 \pi a^2 b) prove area of a disk, radius a, is \pi a^2 c) prove volume of ball, radius a, is \frac{4}{3} \pi a^3 d) prove volume of axisymmetric cone of height h and base with radius...

Ok, so I was eating an apple and I asked myself: If I had two points on the surface and I wanted to find the shortest path between those two points, how would I go about that mathimatically. How about if I had an ellipsoid? Thanks

How do you define curvature for curves on three-dimensional surfaces when the surface is given in the form z=f(x,y)? The resulting formula should be a lot simpler than the one for parametric curves of the form r(t)=(x(t),y(t),z(t)), like it becomes for two-dimensional curves given by y=f(x)...

Homework Statement Reduce the equation to one of the standard forms, classify the surface, and sketch it: 4x = y^2 - 2z^2 Homework Equations The Attempt at a Solution I really don't know what to do for this one because most of the equations I've seen like this involved x^2. Unrelated to...

Homework Statement hi, i am almost done my lab on the coefficient of friction on an inclined plane. I was attempting to prove that the coefficent of static friction would be the same no matter the weight of the mass that was static on the incline. However, i plotted a coefficient versus mass...

Homework Statement Find the set of all points on the surface (y + z)^2 + (z − x)^2 = 16 where the normal line is parallel to the yz-plane. Describe this set. The Attempt at a Solution I find the gradient vector of the surface then I said that the f at f*i should be zero when it is...

Hi all, I'm trying to understand someone's PhD thesis on the topic of variational surface evolution and its application in computer vision, and I'm having trouble working out how he evaluates some particular types of expressions involving the gradient. I think it'll be easier if I specify the...

Homework Statement Please read the attached Homework Equations In the image attached The Attempt at a Solution Thanks a lot

Homework Statement Find an equation describing a surface, and find the surface area Homework Equations Please se the picture attached The Attempt at a Solution Thank you so very much for any help---

The theorem of classification of closed surfaces says that any closed surface is homeomorphic to a fundamental polygon in the plane. I was wondering if any fundamental polygon can be made into a closed surface by adjoining an appropriate atlas to it. The topological requirements of a closed...

Homework Statement Show that the helicoid and the catenoid are conjugate minimal surfaces Homework Equations the helicoid is given by the parameterization X(u,v) = (asinh(v)*cosu, asinh(v)*sinu, au) = (x1, x2, x3) the catenoid is given by the parameterization Y(u,v) = (acoshv*cosu, a...

"A uniform board of length L and mass M lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is (mu1), and in region 2, the coefficient is (mu2). The positive direction is from the region with mu1 to the region with...

Homework Statement If the electric field at a point in space has a magnitude of 300 volts/meter, about how far apart are the equipotential surfaces that differ by 10 volts? well, i think that they are 30 meters apart. All I did was 300 volts/meter/10 volts since that will cancel the...

"Treatment makes surfaces self-cleaning" I read this article, a few weeks ago http://www.engineerlive.com/european-design-engineer/instrumentationelectronics/17068/treatment-makes-surfaces-selfcleaning.thtml Do anyone know more about this? Can it actually be applied to metal? i.e...

Homework Statement I am wondering what the set of area vectors for a surface would be. For a plane on the xy-plane, I know the set of area vectors is <0,0,dx*dy>. Homework Equations So, for a set of points (x,y,z) that make a paraboloid, if F(x,y,z)=0 then [grad(F)•<dy*dz, dx*dz...

Homework Statement Describe the level surfaces of f(x,y,z) = z + sqrt(x^2 + y^2) The Attempt at a Solution First of all, what is actually a level surface? Just a normal surface in space? I followed an example I found on the internet, and this is my attempt at a solution: First...

Homework Statement Hi, I need help with the following. I'm asked to find the parametric equation of the tangent line to the curve of the interrsection of the paraboloid z = x^2 + y^2 and the ellipsoid 4x^2+y^2+z^2 = 9 at the point (-1,1,2). Homework Equations I think I'm asked to find...

"The net flux through ANY closed surface surrounding a point charge q is given by q/"permittivity of free space" and is independent of the shape of that surface." I'm having a little trouble understanding this... when my book derived this formula, it did so by using the surface area of a...

I am trying to show that the connected sum of two topological surfaces does not depend on the open discs removed. Any hints?

A block of mass 3.0 kg starts at a height 0.60 m on a plane that has an angle of 30 degrees from the horizontal. Upon reaching the bottom, the block slides along a horizontal surface. If the coefficient of friction on both surfaces is 0.20, how far does the block slide on the horizontal surface...

The question reads: Identify the following surfaces given that k, l, m, n are fixed values and \hat{u} is a fixed unit vector. a) |\overrightarrow{r}|=k b) \hat{r}\cdot \hat u=l c) \overrightarrow{r} \cdot \hat{u} = m|\overrightarrow{r}| for -1 \leq 1 d)|\overrightarrow{r} -...

According to Presley (Elementary differential geometry), "A smooth surface is a surface \mathbf{\sigma} whose atlas consists of regular surface patches." (The atlas of a surface is a collection of homeomorphisms that "cover" it. A surface patch is just another word for an homeomorphism in the...

Not really a homework problem, but I'm having a hard time with this section. It's mostly dealing with the horizontal component of the force. This is from my book, Fluid Mechanics by frank m white 5 th ed, "The horizontal component of force on a curved surafce equals the force on the plane...

I'm looking for a good tensor reference book that provides insights into the following areas of tensors: 1. Symmetries & how to extract them. 2. Full tensor visualisation eg. how to visualise the stress tensor in its 9 component form without resorting to a split into 3 simultaneous...

What is the flux though each of the surfaces: I got: Surface 1: -q/ε Surface 2: -q/ε Surface 3: 0 Surface 4: 0