Cylindrical Definition and 761 Threads

Homework Statement I must calculate the capacitance of the following capacitor : A cylindrical capacitor made of 2 shells (not sure if shell is the right word in English. Made of 2 cylinders maybe), one of radius a and the other of radius b>a. It has a length of L. We introduce entirely...

Can anyone help with the solution of the Laplace equation in cylindrical coordinates \frac{\partial^{2} p}{\partial r^{2}} + \frac{1}{r} \frac{\partial p}{\partial r} + \frac{\partial^{2} p}{\partial z^{2}} = 0 with Neumann no-flux boundaries: \frac{\partial p}{\partial r}...

Homework Statement A conducting wire carrying a charge \lambda per unit length is embedded along the axis of the cylinder of Class-A dielectric. The radius of the wire is a; the radius of the cylinder is b. Show that the bound charge on the outer surface of the dielectric is equal to the...

Homework Statement Use cylindrical coordinates to evaluate the triple integral \int\int\int \sqrt{x^2+y^2} dV in region E where E is the solid bounded by the circular paraboloid z=9-(x^2+y^2) and the xy-plane. Homework Equations knowing that x = rcos\theta y= rsin\theta z=z...

cylindrical cordinace?? Homework Statement this is a two part question and is multiple choice part 1 Determine the type of the solid described by the given inequalities. 0 ≤ r ≤ 4, - pi≤ θ ≤ pi, -sqrt(16 − r^2) ≤ z ≤ sprt(16 − r^2) a half-cylinder a cylinder a...

Homework Statement Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and height h. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Homework Equations E =...

Hello there, i wanted to know what is the difference between a surface in R^2 and a surface in R^3 in an xyz cordiante system. More specifically how do they look like? an example please. Is this different from a 2 dimensional surface and a 3 dimensional surface respectively. Also what...

Homework Statement Hey guys, My prof asked us to find the radius of a cylinder within a cylindrical capacitor with 2 radii a and b. I know we use the Capacitance formula for a cylinder but I can't seem to get pass the q that shows up when I plug it into the 1/2 c*V^2 EDIT: He wants us to find...

Jackson 3.12: An infinite, thin, plane sheet of conducting material has a circular hole of radius a cut in it. A thin, flat disc of the same material and slightly smaller radius lies in the plane, filling the hole, but separted from the sheet by a very narrow insulating ring. The disc is...

i need help transforming this equation into cylindrical coordinates... w = omega i = i hat j = j hat k = k hat r is a vector r(t) = Asin(wt)i + Bsin(wt)j + (Ct - D)k where w, A, B, C and D are constants. i, j, and k are throwing me off...i know they are components of x, y and z...and i know...

Homework Statement A cylindrical air capacitor with a length of 12.2 m stores an amount of energy equal to 3.00E-8 J when the potential difference between the conductors is 4 V. Calculate the magnitude of the charge on each conductor. Homework Equations...

I have picked up "Roark's Formulas for Stress and Strain" and "Mechanical Vibrations" and have been unable to reach resolution on a particular problem. I am interested in the behavior of a uniform cylindrical shell (cylinder diameter >> wall thickness) rigidly clamped at both ends wherein...

Homework Statement A vector field A is in cylindrical coordinates is given. A circle S of radius ρ is defined. The line integral \intA∙dl and the surface integral \int∇×A.dS are different. Homework Equations Field: A = ρcos(φ/2)uρ+ρ2 sin(φ/4) uφ+(1+z)uz (1) The Attempt at...

Hey Guys, I wanted to clarify something I'm not too sure about. The charge inside (in the center not actually in the shell) of a charged non-conductive spherical or cylindrical shell is zero, am I wrong? The reason being the geometry within the shell cancels all the charges within. Any...

Homework Statement Evaluate using the cylindrical shell method, the volume of the solid of revolution obtained by rotating the region enclosed by the curves y=x^3, y=-x and y=1 around the line y=-1. The attempt at a solution The answer is suppose to be 127(pi)/42 but I keep getting...

Homework Statement A cylindrical cavity oriented along z axis with length of 2 m has a filament in it upon which a current of 10 A is impressed. Cavity is perfectly conducting whereas it is filled with lossy dielectric. Electric field on the cavity is given as: [FONT="Arial...

Homework Statement Find the value of the (surface) integral \int curl \textbf{A} \bullet \textbf{a} if the vector \textbf{A}=y \textbf{i}+z \textbf{j}+x \textbf{k} and S is the surface defined by the paraboloid z=1-x^2-y^2 Homework Equations x=s\cos\phi y=s\sin\phi...

Hi everyone! There's a question bothering me about the two coordinate systems - cylindrical and spherical: Consider the two systems, i.e. (r, \theta, \phi)\rightarrow\left(\begin{array}{c}r\sin\theta\cos\phi\\r\sin\theta\sin\phi\\r\cos\theta\end{array}\right) and...

Homework Statement Immediately outside a very long, cylindrical wire of radius R1=0.6mm, the electric field is 50 kV/m directed towards the wire's surface. The wire is in air. What is the charge per unit along length the wire? (take care with sign) What is the field at R2=3.0mm? (i.e. 2.4mm...

I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that...

Homework Statement A cylinder of length L and radius R is centered on the z-axis in a region where there is a uniform electric field of E i. Determine the flux for the fourth of the cylindrical surface where x > 0 and y > 0. Homework Equations \phi = \int E dS The Attempt at a...

Pseudo forses arising in a frame are defined as the negative of mass times acceleration of the frame used. now in cylindrical coordinate system if we compute acceleration, we should be able to know completely the corilis and centripetel forses. However my problem is I don't understand...

would anybody like to discuss how to accurately follow a particle moving in a HELICAL PATHWAY using vectors, spherical and cylindrical coordinates? I'm not sure how to follow a geometric helical pathway using linear and parametric equations.

The diagram accompanying this post shows a cylindrical column bored at right angles to a flat surface. Let’s say the material is a block of brass with a hole drilled in it. The arrow represents a fast moving stream of compressed air. As the air passes over the top of the column a high pitched...

Is there a cylindrical coordinate system that is centered about the foci of an ellipse. It would include (r,theta,z) just like cylindrical coordinates only for an ellipse. If this coordinate system exists, what is the laplacian? Chris

http://img208.imageshack.us/img208/5153/12802868.png Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

Homework Statement Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm. Homework Equations I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be...

Homework Statement calculate total induced charge on a charged cylinder. where the surface charge density is given by sigma= 2eEo cos(phi) Homework Equations the total induced charge on the cylinder is Integral of (sigma) da can u calculate this integral fo me ... it very...

A closed cyliindrical container has a volume of 5000in^3. The top and the bottom of the container costs 2.50$in^2 and the rest of the container costs 4$in^2. How should you choose height and radius in order to minimize the cost? v=pi(r)^2 Unfortunately my attempt at this problem is...

Homework Statement A cylindrical fishing reel has a mass of 0.85 kg and a radius of 4.5 cm. A friction clutch in the reel exerts a restraining torque of 1.6 N·m if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin with an angular acceleration of 66 rad/s2. a)...

Homework Statement Identify and sketch the graph of the surface y^2 + z^2 = 1. Show atleast one contour perpendicular to each coordinate axis Homework Equations The Attempt at a Solution for the yz plane z = (1-y^2)^1/2 a circle of radius 2 centered at the origin xy, set z=0...

Homework Statement z = 4y^2, x = 0, is rotated about the z axis. write the equation of the resulting surface in cylindrical coordinates Homework Equations The Attempt at a Solution not really sure what the x = 0 means so i ignored it i solved for y because that would be my...

Hi Guys, I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder. Can you please check the limits and integral I have? The cylinder is x^2+y^2= 4 sphere = x^2+y^2+z^2= 9 As its a cylinder...

y=x^4, y=sin(pix/2); about x=-1 the solution is attached . how he determinate it to be from 0 to 1 ...? as I know , we usually put for example the expression of y1 = y2 and solve it for zero but in this case is not easy to do it,so how did he do it...?? note: my english is...

For example with a paraboloid, which do i use? I am also slightly confused with the limits in the integral. If doing a triple integral with drdθdΦ i understand the limits of the dr integral but when it comes to dθ and dΦ i don't understand why sometimes its 0 to 2π or 0 to π etc. For example...

if a cylindrical lens is put in the path of a laser beam what is expected to be seen at its focal plane? how will the beam look like after emerging from it?

Homework Statement The problem was to find the volume enclosed by a sphere of radius "a" centered on the origin by crafting a triple integral and solving for it using cylindrical coordinates. Homework Equations x^{2}+y^{2}+z^{2}=a^{2} : Equation for a sphere of radius "a" centered on...

I am a student at ungku omar polytechnic.i want to ask someone that is good in engineering robot.i want to know how to make the cylindrical robot,do i have to used ball screw or belting as an actuator.I want to a build a small robot only about 550mm long and 650 mm hight.It can pull load of...

can anyone help me in understanding the concept of a cylindrical lens ? how is the imaging by a cylindrical lens different from that of a sphericaL lens? how does one decide to use a particular lens or a system of lenses for image formation? please suggest some good reference for this .. thanx

Hi All, from this page (Cylindrical Capacitor) => http://www.phys.uri.edu/~gerhard/PHY204/tsl105.pdf What happens when L is <= b? Does the computation change? and from this page http://www.physics.umd.edu/perg/abp/TPProbs/Problems/E/E52.htm The capacitor is simplified to a plane...

Homework Statement Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates. Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z ... (divergence in Cartesian coordinates) I need to...

Homework Statement Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin...

Homework Statement Transform to cylindrical coordinates: x^{2}+y^{2}=R^{2} Doesn't look like a problem at all first... :smile: Homework Equations .. after all I know that is a circle (2d) and we can forget the z-axis (=0) and transform it to just polar coords. Also I know, that for...

Convert r=2cos(theta) from cylindrical coordinates to rectangular coordinates I have tried squaring both sides so that it will be equal to x squared plus y squared, and then solving for a variable. No matter what I do though I am left with two variables so I feel like I am taking the...

Homework Statement A long circular rod of radius R, made of conducting material, has a cylindrical hole of radius a bored parallel to its axis and displaced from the centre of the rod by a distance d. The rod carries a current I distributed uniformly over its cross-section. Consider the...

Homework Statement I have two homework problems, both of which require me to solve the equation for the capacitance of a capacitor for the inner radius of the capacitor (one cylindrical, one spherical). This shouldn't be a problem, but I think my algebra is screwy. a = inner radius b = outer...

Homework Statement set up an integral in cylindrical coords to compute the volume of the solid S bounded by the sphere x^2+y^2+z^2=12 and the cone 3z^2=x^2+y^2 where z>=0 The Attempt at a Solution i will post my answer here. please let 'I' stand for integral: i get, I[0,2pi]...

Homework Statement A cylindrical shell of radius 7.00 cm and length 24.0 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the...

I am having trouble understanding the concept of cylindrical symmetry in an infinitely long line. Please picture a finite Gaussian cylinder enclosing a portion of the length of the line, parallel to the line. My book states that there cannot be any component of E perpendicular to the...

Homework Statement Here is my problem. I don't fully understand Gauss' law so any assistance there would be greatly appreciated Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 4.00×10-2 m. The charge density is 1.00×10-2 C/ m3. What is the...