Cylindrical Definition and 761 Threads

hello i am solving heat equation in cylindrical coordinator. i am using MATLAB "pdepe" solver to solve the partial differential equation. can anyone suggest me how to choose the initial condition?

This is a real world project. I'm building a giant roll-up window shade to be used for a special effects green screen. The first real model attempt (without math) failed. See the two pictures of the tube structure being held up by chairs. The only axle was about 3ft of 1.5" pipe at each...

Homework Statement "A cylindrical shell of length 230 m and radius 6 cm carries a uniform surface charge density of σ = 14 nC/m^2. What is the total charge on the shell? Find the electric field at the end of a radial distance of 3 cm from the long axis of the cylinder." Homework Equations...

Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.

Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of...

I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat). While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there...

Homework Statement Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin.Homework Equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/xThe Attempt at a Solution So I know that the equation for the sphere...

Hi, I'm currently in a dead spot of my mini-project where I've to decide upon the coil shape. I can't find adequate definition of both coils by the means of: - size - losses - frequency range - inductance - skin depth which makes it impossible to argue which one would be better...

Homework Statement The figure (found here) shows a cross-sectional view of two concentric, infinite length, conducting cylindrical shells. The inner shell has as an inner radius of a and an outer radius of b. The electric field just outside the inner shell has magnitude E0 and points radially...

Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...

There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant. Question...

Homework Statement I don't have a specific problem in mind, it's more that I forgot how to solve the particular equation from first principles. \nabla^{2} \Phi = k^{2}\Phi Places I've looked so far have just quoted the results but I would like the complete method or the appropriate...

Homework Statement I must get the first eigenvalues of the time independent Schrödinger's equation for a particle of mass m inside a cylinder of height h and radius a where ##h \sim a##. The boundary conditions are that psi is worth 0 everywhere on the surface of the cylinder. Homework...

Homework Statement I'm trying to get to grips with Godel's 1949 Paper on Closed Time-like Curves (CTCs). Currently I'm trying to confirm his transformation to cylindrical coordinates using maple but seem to keep getting the wrong answer. Homework Equations The line element in cartesian...

Hi all, I was wondering how would one go about converting a displacement vector in cartesian coordinates to cylindrical. I am getting a bit confused on how to deal with the unit vectors; converting a point in space is a simple task, but when it's a vector it just confuses me. I am specifically...

Homework Statement The intensity produced by a long cylindrical light source at a small distance r from the source is proportional to a)\frac{1}{r^2} b)\frac{1}{r^3} c)\frac{1}{r} d)None of these Homework Equations I=\frac{dF}{dω} I is the intensity, dF is the luminous flux of the...

Homework Statement Let W= {(x,y,z)| x^2 + y^2 ≤ 1, -1 ≤ z ≤ 1} (W is a bounded cylindrical region) Evaluate the triple integral f(x,y,z)= z^2 x^2 + z^2 y^2 over W. Use cylindrical coordinates Homework Equations i don't see any relevant equations besides the obvious cylindrical...

Homework Statement A solid metal cylinder of radius R and length L, carrying a charge Q, is surrounded by a thick coaxial metal shell of inner radius a and outer radius b. The shell carries no net charge. Find the potential at the center, using r=b as the reference point. Homework...

Homework Statement Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method. x^2 + (y-1)^2 = 1 Homework Equations Cylindrical method: ∫2∏xf(x)dx Slice Method: ∫A(x)dx The Attempt at a Solution x^2 + (y-1)^2 = 1 x =...

Homework Statement In a cylindrical container (with radius R) there are 2 fluids (separated like water and oil, fluid 1 lies under fluid 2) with given volumes V_i, given densities ρ_i. You let them rotate with respective angular frequencies ω_i. There is no friction. Find the functions of...

Homework Statement Hi The expression for the magnetic field from an infinite wire is \boldsymbol B(r) = \frac{\mu_0I}{2\pi}\frac{1}{r} \hat\phi which points along \phi. I am trying to convert this into cartesian coordinates, and what I get is \boldsymbol B(x, y) =...

I recently had a problem set with two questions that seemed to give very similar answers. I'm not asking how to do this, so I don't think this post belongs in the homework section. Rather, I'm asking if the similarity I think I see has any deeper meaning in the physics of electric fields...

Hi I would like to know is there any way except using graph to find area element in cylindrical ( or Spherical) coordinate system? Thanks.

From this equation x2 + y2 = 2y I was wondering how in the solutions manual it was decided that 0≤z≤1 ? Edit: Don't read... I was looking at a solution to a different problem

Homework Statement The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z) Homework Equations No clue The Attempt at a Solution No clue

Homework Statement As a part of bigger HW problem, I need to calculate the integral: \oint[\hat{r}+\hat{z}]d\phi Homework Equations The Attempt at a Solution In cylindrical coordinates: =[\hat{r}+\hat{z}] \ointd\phi =2∏[\hat{r}+\hat{z}] On the other hand if I convert it to...

Homework Statement Hi, I'm having a tremendous amount of difficulty with finding the radii in problems using cylindrical shells. Here's the question: find the volume of the solid found by rotating the region bounded by the given curves: x = y2+1, x = 2, about y = -2 I got 2 -...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

The problem states: From the field with a radial cylindrical component only given by the following equations: E(r)= (ρ0*r3)/(4 * ε0*a2) for r<=a E(r)= (ρ0*a2)/(4*ε0*r2) for r > a obtain the corresponding charge distribution in free space in which the equation is: ρ(r) = ρ0*(r2/a2)...

Homework Statement Convert the following as indicated: 1. r = 3, θ = -π/6, φ = -1 to cylindrical 2. r = 3, θ = -π/6, φ = -1 to cartesian The Attempt at a Solution I just want to check if my answers are correct. 1. (2.52, -π/6, 1.62) 2. (-2.18, -1.26, 1.62)

Homework Statement 1.21 Express in cylindrical components: (a) the vector from C(3, 2,−7) to D(−1, −4, 2); (b) a unit vector at D directed toward C; (c) a unit vector at D directed toward the origin. I just want to know (a). And the solution from the book is attached, too...

Homework Statement I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help! The Attempt at a Solution Spherical(cylindrical) r=(ρ^2+z^2)^(1/2)...

Homework Statement https://dl.dropbox.com/u/64325990/cylindrical.PNG The Attempt at a Solution Okay so I found r = 2.24 and z = -3. However I am stuck at finding theta. I think I just don't understand what the question means when it says "In addition, the line defined by theta = 0 in...

Hi there, I arrived at the solution for a electric potential problem for a semi-infinite cylinder (there was a potential distribution given for the boundary conditions but that's not important here). http://i210.photobucket.com/albums/bb283/DidgeFrank/Cylinder_pot.jpg The solution is...

Homework Statement The problem is attached in the picture. The Attempt at a Solution What bothers me is that they say the wedge is bounded by x + z = a. Doesn't this imply that the calculated volume should only be half of what is written in the answers? I'm aware that the plane x +...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = \sqrt{x-1} , y = 0, x = 5; about y = 3 The Attempt at a Solution I already completed graphing it, but not really sure how...

If a cylindrical vacuum chamber's diameter is increased, then the inward force on the two ends will increase because the area is increased. However, if the length of the chamber is increased, while keeping diameter constant, will that increase the net inward force on the chamber? Or does...

Cylindrical lenses focus light rays onto a line instead of a point. Is that means several images will be formed from a point object aftering passing through the lens? (please see the attached files 1 and 2) If I am correct, can anyone explain to me,when you add water to a tall water...

is there any way to find vector in cylindrical system without converting the variable of cylindrical system to Cartesian system? advanced thanks

Homework Statement A cylindrical metal bar of length L hangs by two strings in a horizontal position. The metal bob of a simple pendulum hits one end of this metal bar in a direction perpendicular to the crossection of the bar. Find an expression for the time t of contact during the impact...

Homework Statement I don't really understand something in my textbook. It says the heat Resistor (how to say that in English? I hope it's alright like this...) trough a cylindrical tube (from the inside to the outside or revers) would be: R(heatrisistor)=1/2∏Lλ * ln (R1/R2) And then my...

Homework Statement Consider a long cylindrical coaxial capacitor with an inner conductor of radius a, and outer conductor of radius b, and a dielectric with a relative electric permittivity or dielectric ε(r), varying with the cylindrical radius. The capacitor is charged to the voltage V...

Homework Statement A long cylindrical insulating shell has an inner radius of a = 1.37 m and an outer radius of b = 1.60 m. The shell has a constant charge density of 2.70 10−9 C/m3. The picture shows an end-on cross-section of the cylindrical shell. What is the magnitude of the electric...

Homework Statement Find limits of integration for volume of upside down cone with vertex on origin and base at z=1/sqrt(2). Angle at vertex is pi/2. Do this in cylindrical coordinates. Homework Equations None. The Attempt at a Solution My inner integral conflicts with the books...

I recently did an integral of the form: ∫∫1/ρ dρρdθ the extra ρ between dρ and dθ is the cost of switching to cylindrical coordinates. Now I want to know, do you carry out the integration in ρ, keeping the ρ outside the integration (since it's technically a scaling factor that belongs to...

Homework Statement In a textbook it states: How do they conclude this? Thank you. Homework Equations The Attempt at a Solution

I'm looking for a function to plot things in 3D using cylindrical coordinates but apparently Mathematica doesn't have one?

Homework Statement The outer conductor (radius b, length l) of a long cylindrical capacitor is earthed. The inner conductor (radius a, length l) is hollow, insulated and uncharged. A sphere of radius R is charged to a potential V far from any other bodies and is inserted inside the inner...

(2.16) A long coaxial cable carries a uniform volume charge density ρ on the inner cylinder (radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). This surface charge is negative and just the right magnitude so that the cable as a whole is electrically...

Homework Statement The temperatur at the point (x,y,z) in a substance with conductivity K=6.5 is u(x,y,z)=2y2+2z2. Find the rate of heat flow inward across the cylindrical surface y2+z2=6, 0≤x≤4. Homework Equations F=-k∇u -k∫∫s∇u*ds The Attempt at a Solution So F=-6.5(0,4y,4z) I...