Cylindrical Definition and 821 Threads

Homework Statement Suppose the magnetic field line pattern is cylindrical symmetric. Explain with Stokes theorem that the field decreases like 1/r (with r the distance from the axis of the cylinder). Homework Equations Stokes theorem The Attempt at a Solution I was thinking of a circular loop...

Here is a sketch of the region to be rotated around the y axis. You first need to visualise this entire region being rotated around the y axis, to get a mental picture of what the solid looks like. Then you need to imagine that the solid is made up of very thin vertically-oriented hollow...

Here is a sketch of the region to be rotated. To find a volume using cylindrical shells, you first need to picture what the region would like like when that area is rotated around the y axis. Then consider how it would look if that solid was made up of very thin cylinders. Each cylinder has...

Homework Statement Here is my question Homework Equations I don't know with what formula does the book find Fourier series? The Attempt at a Solution

I am trying to find the electric field of a hollow, open-ended, thin-walled cylindrical conductor. I am trying to solve something regarding LINACs: Assume we have an isolated, hollow, open-ended, thin-walled cylindrical conductor, with a net charge. The net electric field within the...

Homework Statement Consider a long, cylindrical charge distribution of radius R with uniform charge density ρ. a) Using Gauss’s law, find the electric field at distance r from the axis, where r < R b) Using Gauss’s law, find the electric field at distance r from the axis, where r > R...

Homework Statement The figure shows a cross section across a diameter of a long cylindrical conductor of radius a = 2.92 cm carrying uniform current 151 A. What is the magnitude of the current's magnetic field at the center of the conductor? Homework Equations Biot-Savart's Law The Attempt...

Homework Statement Using the cylindrical polar co ordinates ##(ℝ,θ,z)## calculate the gradient of ##f=ℝ sin θ + z^2## the textbook says that the scale factors are ## h1=1, h2=ℝ & h3=1## how did they arrive at this?[/B]Homework EquationsThe Attempt at a Solution ##h1=|∂f/∂ℝ|= sin θ...

Homework Statement An open cylindrical tank of acid rests at the edge of a table 2.20\cdot 10^0\ m above the floor of the chemistry lab. If this tank springs a small hole in the side at its base, how far from the foot of the table will the acid hit the floor if the acid in the tank is...

Here is some background to the problem (in a stirred tank): "With yield stress non-Newtonian (viscoplastic) fluids, it is possible to generate an agitated volume around the impeller, defined as a cavern, surrounded by a stagnant region where the shear stress is insufficient to overcome the...

Homework Statement Determine the center of mass in cylindrical coordinates of a cone with constant density ##\rho(\vec{r})##. (The cone is inverted, i.e. it's thinnest point is at ##z=0##.) Homework Equations ##m=\int\int\int_C \rho r \, drdzd\theta## ##\overline{r}=\int\int\int_C r\cdot r\...

Homework Statement There is liquid in a cylindrical container at some level. Now when the container is heated, the level of the liquid remains the same in the container. What is the relationship between the coefficient of linear thermal expansion of liquid and the container ? Homework...

Hello! (Wave) How can we find what section of the cylinder $x^2+y^2=1$ corresponds to cylindrical points $(1,\theta,z)$ in the range $\theta$ in $[0,\pi]$ and $z$ in $[ -1,1]$ ? We have that the cylindrical points are of the form $(r, \theta, z)$ where the following relations hold: $$x=r...

Homework Statement A circular cylindrical barrel is half full with oil. If the diameter of the base is 8.0 m, find the net force against each end if ρo = 800 kg/m3. The cylinder is on its side. Homework Equations F=P*A P=ρgdy The Attempt at a Solution P = ρo*g*h, where h is the radius which...

Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...

Homework Statement [/B] A semiconducting nanowire has a volume charge density ρ(r)=ρ0(r/R) where R is the radius of the nanowire. How would you calculate the electric field inside the wire? Homework Equations Gauss's Law The Attempt at a Solution [/B] I know that by symmetry the E field...

Homework Statement Sketch each of the following vector fields. E_5 = \hat \phi r E_6 = \hat r \sin(\phi) I wish to determine the \hat x and \hat y components for the vector fields so that I can plot them using the quiver function in MATLAB. Homework Equations A cylindrical coordinate...

Homework Statement The resistance of a wire (conductor) in cylindrical form is: A Disproportional with the length of the wire (conductor) B Disproportional with the square of the wire (conductor) section C Proportional with the square of the length of the wire (conductor) D Proportional with...

Homework Statement A cylindrical conductor with a circular cross section has a radius a and a resistivity ρ and carries a constant current I. What is the flow of energy into the volume occupied by a length l of the conductor? Discuss why the energy dissipated in a current carrying conductor, due...

Homework Statement what's the difference between zs and hc ? in the pictuire , they are both drawn from the bottom of water to the free surface ... Homework EquationsThe Attempt at a Solution [/B]

Hi this isn't my homework, but it is taken from a worksheet for a Maths course(trying to refresh my rusty math), so I hope it fits in here. 1. Homework Statement two cylindrical polar vectors with same origin: P(2,55°,3); Q(4,25°,6) units in m Homework Equations a) Express in cartesian...

Hello everyone! I recently saw a problem about some ice in 2 containers. So: We have 2 vertical cylindrical containers, which have perfect insulating walls, one with surface of the base S and the other one 2S , filled with the same mass of ice. The question is if there is any diffrence between...

Can somebody provide a solution for this question? convert 3 dimensional unsteady compressible NS equations to axisymmetric 2 dimensional incompressible laminar form for a cylindrical pipe, then make a derivation of streamwise velocity profile u(r) using the appropriate boundary conds. thanks

Homework Statement \vec J_b = 3s \hat z \int \vec J_b \, d\vec a I need to solve this integral in cylindrical coordinates. It's the bound current of an infinite cylinder, with everything done in cylindrical coordinates and s is the radius of the cylinder. The answer should end up with a phi...

Rigid body rotating about a fixed axis with constant $\omega$ along the z axis. Express position vector $\vec{r}$ in cyl. circ. cords and using cyl. circ. cords find (a) $\vec{v}=\omega \times \vec{r}$ (b) $\nabla \times \vec{v}$ So $ \vec{r} = \vec{\rho}\rho + \vec{z}z $ (a) =...

Homework Statement I'm doing a question that requires me to take the dot product of 2 vectors in spherical coordinates. Both vectors have only an r component, can I just multiply the r components? Homework EquationsThe Attempt at a Solution

Homework Statement I'm suppose to verify the given Laplace in (a) Cartesian (b) Sperical and (c) Cylindrical coordinates. (a) was easy enough but I need to know if I'm doing (b) and (c) correctly. I don't need a solution, I simply need to know if the my Spherical formula is correct, my...

In my physics lab, I am asked to calculate the volume of a hollow cylinder. The equation for the volume hollow cylinder below was given. Then, my curiosity made me wonder, is the volume of the hollow cylinder the same as the volume of a cylindrical shell used in calculus? At first though you...

Hi everyone My professor just asked us a question that I can't get my head around. So we have the original vector in Cartesian format, <y^2,z^2,x^2> Then I am asked to convert to cylindrical coordinates: z= z; θ==arctan(z^2/y^2); r = \sqrt(y^4+z^4) However , I am then asked to take the...

Homework Statement OK, I thought once I knew what the question was asking I'd be able to do it. I was wrong! Consider the volume V inside the cylinder x2 +y2 = 4R2 and between z = (x2 + 3y2)/R and the (x,y) plane, where x, y, z are Cartesian coordinates and R is a constant. Write down a triple...

I am simulating electrons inside a cylindrical well like the one shown on the first figure. My current work has been on solving the Schrodinger equation numerically for the above potential and then finding corrections to the solution such that it is consistent with Poissons equation. To do so...

Homework Statement Translate the following equations from the given coordinate system into equations in each of the other two systems. Also, identify the surfaces so described by providing appropriate sketches. Homework EquationsThe Attempt at a Solution For my solutions, I obtained z=2r^2 for...

Homework Statement Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^2+y^2} is the cylindrical coordinate. From the three-dimensional heat equation derive the equation U_t=k(U_{rr}+2U_r/r)...

Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from...

Hello, PF! I have some doubts about setting up shell balances in a cylindrical geometry. Consider a fluid flowing down a vertical pipe. In order to perform the momentum balance, we take a cylindrical (annular) shell of length L and width Δr. The analysis of such system can be found in chapter 2...

hello, I am trying to calculate the location of the center of pressure for a non slender cylinder with a cone shapes nose. Referencing the internet and notes from a aerodynamics course, all the methods are for slender bodies. unfortunately, my body is not slender. I am reluctant to go to CFD...

Hello all, I am doing homework and have come upon this question: A cylindrical hole is drilled all the way through the center of a sphere (as shown in the figure below). Show that the volume of the remaining solid depends only on the length L of the hole, not on the size of the sphere. Figure...

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...

Homework Statement a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3? b) What is the magnitude of the electric field as a radial distance of r = 20 d? I was able to determine the...

Homework Statement Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system. Homework Equations Capacitance per unit length, C'=Q'/U Gauss law, cylindrical...

Hello! While studying from the book 'Fluid Mechanics' by Cengel I came across the section which explains the behavior of fluids acting like a rigid body when the cylindrical container which contains the liquid rotates with a uniform angular velocity. Without much explanation the author states...

Homework Statement Find potential and charge per unit length of every cylindrical hollow shell if the outer shell is grounded. The length is considered to be infinite. Homework Equations V=∫Edl The Attempt at a Solution I am not sure how to derive potentials for first two conductors...

A florist delivers single stemmed flowers in a sealed plastic container that is cylindrical in shape. Each container has a bade radius of 4cm and a height of 45cm. the florist wished to decorate each container with a very thin coloured ribbon. The ribbon will wind around the body of the...

Given an energy functional $ E=\int_{0}^{\infty} \,dr.r\left[\frac{1}{2}\left(\d{\phi}{r}\right)^2 - S.\phi\right] $ I am told that discretizing on a lattice ri=ih (h=lattice size, i is i axis) leads to : $ 2{r}_{i}{\phi}_{i} - {r}_{i+\frac{1}{2}}{\phi}_{i+1} - {r}_{i-\frac{1}{2}}{\phi}_{i-1}...

Homework Statement A beam of thermal neutrons (10^12 neutrons per cm^2 second) strikes a 1cm thick water target normal to its surface. The target is a round disk with diameter 20cm. Find the exposure rate (R/second) 100cm beyond the water target (the middle of the disk) from only the...

Homework Statement An infinitely long cylindrical surface of circular cross-section is uniformly charged lengthwise with the surface density σ = A cosΦ where Φ is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the the given surface. Find the...

Given the equation for a Gaussian as: ##z = f(x,y) = Ae^{[(x-x0)^2 + (y-y0)^2] /2pi*σ^2 }## , how would I go about converting this into cylindrical coordinates? The mean is non-zero, and this seems to be the biggest hurdle. I believe I read earlier that the answer is ~ ##z = f(r,θ) =...

Hi, I was wondering if anyone could help with a vector question that I have. If I have a unit vector defined in cartesian co-ordinates as p= (0,1,0) how would I go about converting this vector to a cylindrical geometry. I understand that I will probably need to use p_r=sqrt(px^2+py^2) and...

Where can I find and how can I derive the orthogonality relations for Hankel's functions defined as follows: H^{(1)}_{m}(z) \equiv J_{n}(z) +i Y_{n}(z) H^{(2)}_{m}(z) \equiv J_{n}(z) - i Y_{n}(z) Any help is greatly appreciated. Thanks

Homework Statement We have two coaxial cylinders with radius r0 and r1. The space between the two cylinders is completely coverd with two coaxial isolation layers with relative dielectric constants ε1 and ε2, ε1 is for the inner layer. Calculate the thickness of the inner layer such that the...