Cylindrical Definition and 761 Threads

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...

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...

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

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...

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...

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?

Homework Statement Homework Equations The Attempt at a Solution I'm not sure what is being varied here, radial separation between capacitors x = (b-a) or whether the capacitors can slide up and down so as to change the length L of the capacitor..

Dear All, I did post this issues in the physics forum, however there is somebody ask me to post it in the engineering forum. With this I re-post it here. Does anyone here familiar with a theory called Principal Virtual Work (Equilibrium theory) ? I read somewhere that with this theory, i...

Dear All, Does anyone here familiar with a theory called Principal Virtual Work (Equilibrium theory) ? I read somewhere that with this theory, i could relate(for pipeline application - collapse & buckling) the components for ovalisation, external pressure and hoop strain. Appreciate if...

1. Homework Statement [/b] A solid cylindrical conducting shell of inner radius a = 4.9 cm and outer radius b = 6.1 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 7.4 A in the positive z-direction. An inifinte conducting wire is located along...

Homework Statement The current density of a cylindrical conductor of radius R varies as J(r) = J0e−r/R (in the region from zero to R). Express the magnitude of the magnetic field in the regions r < R and r > R. (Use any variable or symbol stated above along with the following as necessary...

Homework Statement Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis. Homework Equations How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful. The...

Homework Statement A copper resistor has the shape of a cylindrical shell. What is the resistance of this resistor if its length is 1m, its inner radius is 0.1cm, and its outer radius is 0.2 cm? What is the radius of a solid wire of circular cross section with the same length and the same...

Homework Statement Two very long coaxial cylindrical conductors are shown in cross-section above. The inner cylinder has radius a = 2 cm and caries a total current of I1 = 1.2 A in the positive z-direction (pointing out of the screen). The outer cylinder has an inner radius b = 4 cm, outer...

Is the energy of a rotating cylindrical spacecraft conserved when a point-like astronaut climbs up a spoke connecting the walls with the center of the cylinder? If so, when I calculate the fractional change in apparent gravity at the walls when the astronaut reaches the middle I get different...

Homework Statement The picture of the problem can be found here: http://www.2shared.com/photo/U_JIkDks/Capture.html The questions that I'm having trouble with are: (a) The magnitudes of the charge densities on the inner and outer shells are now changed (keeping λinner = -λouter) so that...

Homework Statement a cylindrical solid of charge q, radius R, and length H. The Gaussian surface S is a cylindrical shell of radius r and length h, with r < R. Determine the net electric flux given that q = -48Q, R = 4L, H = 3L, r = 2L, and h = 2L (type the integer value, along with the sign...

Homework Statement Find the volume of the solid that lies between z=x2+y2 and x2+y2+z2=2 Homework Equations z=r2 z=√(2-r2) The Attempt at a Solution So changing this into cylindrical coordinates, I get z goes from r2 to √(2-r2) r goes from 0 to √2 theta goes from 0...

Hi, could anyone tell me a reference on Navier-Stokes equation for the COMPRESSIBLE flow in CYLINDRICAL coordinate? Just can't find a good reference book. Thanks in advance. Jo