Cylindrical Definition and 821 Threads

Hello all! Homework Statement Consider a cylindrical cavity with length "d" and radius "a". Find the corresponding electric field, and the dispersion relation therein. Homework Equations Maxwell's equations. The Attempt at a Solution I tried to solve the appropriate vector Helmholtz...

Homework Statement Part (a): Under what circumstances do these equations work? Part (b): Find Temperature as a function of x, in steady state. Part (c): Show heat loss is proportional to r^1.5 Part (d):Assume A = 0, show solution works, and find γ.Homework Equations The Attempt at a Solution...

Hi PF, I posted this in HW a week ago and got no response. Might be a bit beyond the typical HW forum troller. So, please excuse the double-post. Homework Statement I'm trying to derive the rate-of-strain tensor in cylindrical coords, starting with the Christoffel symbols. Homework...

Homework Statement Use cylindrical coordinates to find the volume of the solid that the cylinder r = 3cos/theta cuts out of the sphere of radius 3 centered at the origin. Homework Equations Why do we evaluate theta from 0 to pi instead of from 0 to 2pi? Don't we want to go all the...

I need to use coulombs law to describe the electric field due to a point charge in cylindrical co ordinates. I know the answer should have E = [ρ,0,z] with the azimuth as 0 but I can't show it using the standard electric field equations. please note I need to use E=q/4πε * r/|r|^3 I'm sorry I...

Homework Statement We want to design a cylindrical vacuum capacitor of a given radius a for the outer cylindrical shell, which will be able to store the greatest amount of electrical energy, subject to the constraint that the electric field strength at the surface of the inner sphere may not...

what are the dimensions of rectangular beam of volume maximum that can be cut from a trunk in diameter "D" and length "L", assuming that the trunk has the shaped of a straight circular cylinder shape? Answer Width =lenght

The sum of the length and the perimeter of base of a postal package to is 60 cm. find the maximum volume: when the package is cylindrical. The answer is 2547 cm3 V cilinder = pir2h and the sum L + L+H = 60 2L + H = 60 solving for H and putting it into the volume i don't get the answer Yeah...

To write the uniform charge density of a disk with radius a in cylindrical coordinates, If we do this form: \rho (x)=\frac{A\delta(z)\Theta (a-\rho)}{\rho} (A is constant that sholud be determined and \theta is step function), we get A=\frac{Q}{2\pi a} and so: \rho (x)=\frac{\frac{Q}{2\pi...

Homework Statement Use cylindrical shells to find the volume of a torus with radii r and R. Homework Equations V= ∫[a,b] 2πxf(x)dx y= sqrt(r2 - (x-R)2) The Attempt at a Solution V= ∫ [R, R+r] 2πx sqrt(r2 - x2 - 2xR + R2) dx I feel like this isn't going in the right direction...

Hi everyone, I've two vectors in cylindrical coordinate - (-1,\frac{3\pi}{2},0),(2,\pi,1) - and I want to find the perpendicular unit vector of these two vector. Basically I'll use the cross product, then I'll find the unit vector by \hat{u}=\frac{\vec{u}}{||\vec{u}||}. But do you I...

So far I have learned about Coulomb's law, the electric field, gauss's law, the electric potential and now capacitance. I feel that although I "know of" these topics, I don't actually "flow with them". Ignoring the math for a second; I want to form an understanding. And I think calculating the...

Homework Statement An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.1) What is λ2, the...

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.. y = -x^2 + 6x - 8, y = 0 so I got -8 to 0 for the integral by plotting the graph... How are they getting 2 to 4? You can't solve that by factoring? And when i...

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis...y = x^3 , y = 8 and x = 0 So my question is: Why did they cube root the y (to be more technical why did they put it in terms of x? I don't...

Quick question, may seem rather dumb - but I just want to make sure of something.. Question: Find the volume of the solid obtained by rotating about the y-axis the region between y = x and y = x^2 so when I am setting up my integral am I correct in saying TOP - BOTTOM i.e. --> \int^1_0 (2\pi...

While doing some ASME code calculations for a pressure vessel subject to external pressure I was wondering what'd be the optimum L/D ratio for a vessel that is subject to buckling under external pressure. For a given volume & Pressure. Could a general L/D ratio be derived or would it change...

Hello, In Cartesian coordinates, if we have a point P(x1,y1,z1) and another point Q(x,y,z) we can easily find the displacement vector by just subtracting components (unit vectors are not changing directions) and dotting with the unit products. In fact we can relate any point with a position...

Let E be the solid inside cylinder y^2+z^2=1 and x^2+z^2=1, find the volume of e and the surface area of e

mechanics -- cylindrical steel pressure vessel Homework Statement A thin-walled, closed-end, cylindrical steel pressure vessel, internal diameter 500 mm and wall-thickness 10 mm, has an internal volume 0.5 cubic metres. Find the additional volume of a compressible fluid that must be pumped in...

1. This is about a lab, we measured times of partial discharge(each 100 ml), and the height from the base to the interface, from a cylindrical reservoir, through a little hole near the base. We must now calculate the theoretical times to compare with the ones measured experimentally, and the...

For the problem attached, I solved it and found the answer for part b : 80.21 s How to get sure or know if the answer is right or not. Thanks

Homework Statement The problem states: Use cylindrical coordinates to evaluate \iiint_V \sqrt{x^2 +y^2 +z^2} \,dx\,dy\,dz where V is the region bounded by the plane z = 3 and the cone z = \sqrt{x^2 + y^2} Homework Equations x = r cos( \theta ) y = r sin( \theta ) z =...

Integrate the function f(x,y,z)=−7x+2y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=sqrt(263/137)x and contained in a sphere centered at the origin with radius 25 and a cone opening upwards from the origin with top radius 20. I...

Homework Statement Find the volume using cylindrical coordinates bounded by: x2+y2+z2=2 and z = x2+y2 Homework Equations Converting to cylindrical coordinates: z = √2-r2 and z = r2 The Attempt at a Solution I figured z would go from r2 to √2-r2 r from 0 to √2 and θ...

Homework Statement x=1+(y-2)^2, x=2. Rotating about the x-axis Homework Equations Volume=(2∏y)(1+(y-2)2(Δy) Limits of integration would be from 1 to 3 2∏∫(y)(1+(y-2)2dy 2∏∫y3-4y2+5y dy The Attempt at a Solution 2∏[y4/4-4y3/3+5y2/2] Plug in the limits and I get 32∏/3. The...

Homework Statement Suppose that in spherical coordinates the surface S is given by the equation rho * sin(phi)= 2 * cos(theta). Find an equation for the surface in cylindrical and rectangular coordinates. Describe the surface- what kind of surface is S? Homework Equations The...

Hi folks, I am having trouble generalizing a well-known problem. Let's say we have a cylindrical cavity inside a conductor, and in this cavity runs a line charge λ. I would now like to know the surface charge density on the inside wall of the cavity, but with the line charge not in the center of...

Consider a solid cylinder of radius R. an varying current of current density δ flows through. what would be self inductance of that cylinder

Hello people, I am doing some work where I need to look at a simplified situation regarding a conductor for which the conductivity distribution does not change along the z-direction of an infinite cylinder. The distribution itself is not symmetric in any way. Presume 2 infinitely long...

Homework Statement Show that in cylindrical coordinates x = \rho cos \theta y = \rho sin \theta z = z the length element ds is given by ds^{2} = dx^{2} + dy^{2} + dz^{2} = d \rho^{2} + \rho^{2} d \theta ^{2} + dz^{2} Homework Equations -- The Attempt at a Solution...

I am asked to compute the Curl of a vector field in cylindrical coordinates, I apologize for not being able to type the formula here I do not have that program. I do not see how the the 1/rho outside the determinant calculation is being carried in? Not for the specific problem - but for...

Problem: Starting from the gradient of a scalar function T(x,y,z) in cartesian coordinates find the formula for the gradient of T(s,ϕ,z) in cylindrical coordinates. Solution (so far): I know that the gradient is given by \nabla T = \frac{\partial T}{\partial x}\hat{x}+\frac{\partial...

1.how and why does a light source in an isotropic medium at INFINITY produces PLANE Wavefronts instead of CIRCULAR Wavefronts as in case , when a light source is in the same isotropic medium but at FINITE distance? 2.how and why does a linear source of light such as a slit illuminated ...

Homework Statement What is the compensation factor for converting dy dx to cylindrical coordinates? Homework Equations None that I know of besides the bottom ones as part of the attempt The Attempt at a Solution So I know that the conversion formulas for going from Cartesian (x,y,z)...

So I've been simulating a really simple geometry using ANSYS Maxwell. It is a cylinder only and I am looking at the \overrightarrow{B} and \overrightarrow{H} fields in order to see their relationship between them when the material is magnetized in the circumferential direction. I used a...

I've have two questions, but if my assumption is incorrect for the first, it will also be incorrect for the second. (in-terms of physics.) For a two dimensional cylinder, using cylindrical co-ordinates (as follows), taking v(subscript-r) => velocity normal to cylinder surface & v(subscript-phi)...

Homework Statement I have a graph 1/x^2=y^2+z^2 where z=rsin(θ) and y=rcos(θ) where 0≤r≤1 and 0≤θ≤2∏ on the zy-plane The end result is attached (sorry, I'm not aware of how to use Latex :[ ) I can kind of understand how they determined the first bounds for the integral: the lowest x...

ITS NOT A HOMEWORK PROBLEM PROBLEM::- THINK OF A CYLINDRICAL SHELL WITH NUMEROUS SPHERICAL HOLES ALL AROUND IT. (FOR EG. http://sell.lulusoso.com/upload/20120317/Underground_Water_Pipe.jpg) HOW TO FIND VOLUME & SURFACE AREA OF SUCH A CYLINDRICAL SHELL. (A GENERALIZED CASE FOR N HOLES AROUND...

Hello. I don't know how to prove that a certain function is a solution to the scalar wave equation in cylindrical coordinates. The scalar wave equation is \left(\nabla^2+k^2\right)\,\phi(\vec{r})=0,which in cylindrical coordinates is...

Homework Statement I have a vector field (which happens to be a magnetic field) H = -\frac{I }{2 \pi r}u\varphi u\varphi is the unit vector which is in the cylindrical coordinate system with only the \varphi component nonzero so it circles around the z-axis. r is the radius of the circle...

Hello, my best problem is about find the integration limits. in cylindrical coordinates- where V is limited by the cylinder y^2+z^2=9 and the planes x = 0, y = 3x and z = 0 in the first octant.

Hello, Consider a cylindrical region (length dr, end area dA) at a distance r from the center of the sun Density =ρ(r) Volume = Length x area = dr.dA (How is the formula for volume of a cylinder works here?) Mass= Density x Volume = ρ(r).dr.dA Now, computing F(grav) =...

Homework Statement find the area of the surface defined by x2+y2=y, with yE[0,4] The Attempt at a Solution I tried setting it up with cylindrical coordinates, but it doesn't work. Why? ∫40∫2pi0r*dθ*dy, where r=√y Is it because my height, dy, has a vertical direction while its...

Homework Statement Let S be the part of the cylinder of radius 9 centered about z-axis and bounded by y >= 0; z = -17; z = 17. Evaluate \iint xy^2z^2 Homework Equations The Attempt at a Solution So I use the equation x^2 + y^2 \leq 9, meaning that r goes from 0 to 3 Since y...

Hi. is there anyone who is familiar with surface wave plasma discharges? I want to solve dispersion equation of surface waves in cylindrical plasma column,numerically,to obtain "phase diagram" and "attenuation diagram" from dispersion equation solving. But this dispersion equation include...

Hello, I am looking to apply to heat equation to a cylindrical rod and solving with explicit finite difference scheme. I have never worked with cylindrical coordinates before, what would be the best way to model this? I am having a hard time understanding the advantage of using cylindrical...

Homework Statement Charged particles, each holding charge q are moving in a cylinderical beam centred on the x-axis with n particles per unit volume. All the particles have the same horizontal velocity v. A) By considering a suitable Gaussian surface, calculate the E-field as a function of...

Homework Statement There is a uniform but variable magnetic field ##\vec{B}=(B_0 t)(-\hat{k})##, in a cylindrical region, whose boundary is described by ##x^2+y^2=a^2##. ##\displaystyle \int_P^{Q} \vec{E} \cdot \vec{dy}## is (see attachment 1) A)0 B)##\frac{\pi}{4}(B_0 a^2)##...

In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?