In geometry, coaxial means that two or more three-dimensional linear forms share a common axis. Thus, it is concentric in three-dimensional, linear forms.
A coaxial cable, as a common example, is a three-dimensional linear structure. It has a wire conductor in the centre (D), a circumferential outer conductor (B), and an insulating medium called the dielectric (C) separating these two conductors. The outer conductor is usually sheathed in a protective PVC outer jacket (A). All these have a common axis.
The dimension and material of the conductors and insulation determine the cable's characteristic impedance and attenuation at various frequencies.
In loudspeaker design, coaxial speakers are a loudspeaker system in which the individual driver units radiate sound from the same point or axis.
A coaxial weapon mount places two weapons on [roughly] the same axis – as the weapons are usually side-by-side or one on top of the other, they are technically par-axial rather than coaxial, however the distances involved mean that they are effectively coaxial as far as the operator is concerned.
I need help with part c.
My solution:
Is there an other way to do this other than dimensional analysis?
P.S "dr an infinitesimal radius", it ofcourse should be dz.
Consider an LC circuit consisting of a parallel plate capacitor and a solenoid inductor in series. The formula for the resonant frequency of this circuit is 1/√(LC) where “L” is the inductance of the solenoid and “C” is the capacitance of the capacitor.
Now consider a high-frequency cavity...
I've found the inductance and capacitance per unit length in a long coaxial cable. I even clearly see that if I multiply the two, I can get the speed of light. How do I begin to find the current wave and its speed though?
The magnetic flux ##\phi_m = \int{BdA}##
The magnetic field of the coaxial cable B = ##\frac{I_{enc} \mu_0}{2\pi r}##
since surface area of a cylinder = ##2\pi rdr L, dA = 2\pi L dr## where L is the length of the coaxial cable
so ##\phi_m = \int{\frac{I_{enc} \mu_0}{2\pi r}2\pi L dr}##?
I've been able to prove the following inequality $$\frac{2\pi\epsilon_0}{\log\left(\frac{b_1b_2}{a_1^2}\right)}\leq C \leq \frac{2\pi\epsilon_0}{\log\left(\frac{a_1a_2}{b_1^2}\right)}$$ but have no clue how to obtain exact value. Can someone check whether this inequality is correct and show how...
Hi,
I have to find the magnetic energy inside a coaxial cable of inner radius ##a## and outer radium ##b##, ##I = I##
By using Ampere's law
if ##r<a##
##B = \frac{\mu_0Ir}{2\pi a^2}##
if ##a<r<b##
##B = \frac{\mu_0I}{2\pi r}##
if ##r>b##
##B = 0##
Then, the energy in a magnetic field ##E_b...
The solution is simple by noting that the total angular momentum of the system is constant. (Though I overlooked this)
Instead, I went ahead analyzing the individual angular momentum of both drums.
Let ##L_a## and ##L_b## be the angular momentum respectively. ##M_a##, ##M_b## be the...
Hi all! I'm new here and hoping someone who knows something about ME or Physics can help me out ... and simple terms would be nice.
I am working with two servo motors and would like to minimize the "kick" they make when starting or stopping since they do it quite frequently. Please excuse my...
At first, I started with the result from an earlier problem regarding the capacitance of a cylindrical capacitor:
$$C=\frac{Q}{V}=\frac{2\pi \varepsilon _0\varepsilon _rl}{ln(R_1/R_2)}$$
$$\Rightarrow V=\frac{Qln(R_2/R_1)}{2\pi \varepsilon _0\varepsilon _rl }$$
Then I used the equation...
The total moment of inertia is:
##I_{tot} = 2 M_1 R^2 + \frac{1}{2} M_2 R^2##
We have ## M_1 = (4 \pi R^2) \sigma ## and ##M_2 = (\pi R^2) \sigma ## , where ## \sigma ## is the density of the disks.
We also know that:
## \sigma = \frac{m}{ \pi 5 R^2} ##
this leads us to say that:
##I_{tot} =...
To find ##\sigma_b## I can use a Gaussian surface of a cylinder of length ##L## and radius ##c>r>b##. Since that is inside of the outer conductor, I know the electric field is zero, so I have from Gauss' Law, $$0=2 \pi L\left(b\sigma_b+a\sigma\right)$$ and easily solve for ##\sigma_b##. For...
Image 1: Image 2:
I am attempting to learn about transmission lines and am having problems with this homework problem.
For part a, I have derived an equation for the maximum electric field within the dielectric. I came up with: with r being the radius and the electric field decreasing with...
V(ρ) = V_o*ln(ρ/0.0018)/ln(45/180)
(Attached picture is where the unit vector of r is really ρ.)
In cylindrical coordinates
∇V = ρ*dV/dρ + 0 + 0
∇V =derivative[V_o*ln(ρ/0.0018)/1.386]dρ
∇V = V_o*0.0018/(1.386*ρ)
E = V_o*0.0012987/ρ
Work = 0.5∫∫∫εE•E dv
Bounds: 0.0018 to 0.00045 m
D = εE =...
Homework Statement
This is the exercise 10.6 from Feynman lectures on Physics 2.
Two coaxial pipes of radii a and b(a<b) are lowered vertically into an oil bath. If a voltage V is applied between the pipes, show that the oil rises a height H.
Show that H=(V^2)(κ-1)ε_0/[ln(b/a)ρ(b^2-a^2)g]
where...
Homework Statement
For a medium of conductivity ##\sigma##:
$$ \nabla^2 \vec{B} = \sigma \mu \mu_0 \frac{\partial \vec{B}}{\partial t} + \mu \mu_0 \epsilon \epsilon_0 \frac{\partial^2 \vec{B}}{\partial^2 t} $$
A long solenoid with ##r=b## has n turns per unit length of superconducting wire anc...
I want to expose something that caused me a lot of curiosity. First of all, I beg you to point out my mistakes and, if there are any insurmountable ones, help me to understand them. I start by presenting a figure.
It is a solenoid that differs from the common case, because the wire at one end...
Homework Statement
Coaxial cable has radius a of copper core and radius b of copper shield. Between there is an isolator with specific resistance ζ. What is the resistance of this cable with length L between the core and the shield?
Homework Equations
First, I tried to solve this like this...
Homework Statement
A portion of a long, cylindrical coaxial cable is shown
in the accompanying figure. A current I flows down the
center conductor, and this current is returned in the outer
conductor. Determine the magnetic field in the regions (a)
R ≤ r1, (b) r2 ≥ R ≥ r1, (c) r3 ≥ R ≥ r2, and...
In my lab we are working with a Coaxial coil and stainless steel tube, and are aiming to find the mutual Inductance. I've done some looking around and have easily found the Inductance of a Coaxial cable, and for that of Coaxial coils, but am having trouble with a combination of the two.
The...
Good day All,
I have a confusion in my mind and i hope to clear it
If we use the Amper law to calculate the magnetic field outside the cable, the value would be 0 because the electric current inside the amperian loop is equal to 0,
but in case we apply the Biot savart law to calculate the...
Homework Statement
A coaxial transmission line consists of an inner cylindrical conductor of radius a = 1 mm and a
cylindrical outer conductor chosen to make the characteristic impedance 75 ohm. The space
between the conductors is lled with a gas which can stand a maximum eld of 105 V/m
without...
Homework Statement
An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the...
Homework Statement
Consider a coaxial cable which consists of an inner cylindrical conductor of radius R1, and a shell cylindrical conductor of radii R2 and R3. The 2 conductors are separated with a dielectric material of permittivity ε. Consider the length of the cable, ℓ, much larger than R3...
To calculate the displacement current in a coaxial cable (with equal and opposite currents on the inner and outer conductors), most standard texts use the magnetoquasistatic approximation, which ignores the time-varying electric field term in Ampere’s Law.
Using this approximation, the...
Homework Statement
Two coils of the same length and almost the same cross-section are put one inside the other.
Find their mutual inductance if the self-inductances are and .
Homework Equations
1) \phi_i=L_i I_i
2) \phi=\iint_A \vec{B} \cdot d\vec{A}
3) \phi_1=M_{12} I_2
The Attempt at...
Hi, for a particular project, I would like to create a 1~2 Tesla magnetic field in a stainless steel pipe along the z axis. I was wondering if my concept would work, or if anyone had better ideas.
Here's my concept.
Fig1. So I got a few pipes about 1 inch in diameter. I would like to have a...
As part of an ongoing project I have been working on, I have been reading through J.J. Thomson's Cathode Ray Experiment. As part of his setup Thomson writes, "The arrangement used was as follows: — Two coaxial cylinders (fig. 1) with slits in them are placed in a bulb connected with the...
hi guys, i don't really have a good background on mechanical engineering so i was hoping that someone would help me.
i don't really get how coaxial rotors work, i saw a couple of videos and read a couple of papers on it but what i don't get is that can one motor rotate one shaft in opposite...
Homework Statement
A thin hollow cylinder of radius a is surrounded co-axially by another hollow cylinder of radius b, where b>a. An electric current I flows through them (I is into the plane of paper (x) in outer cylinder and coming out of plane of paper (.) in inner cylinder). Find the:
a)...
1. Homework Statement
An air coaxial transmission line has a solid inner conductor of radius a and a very thin outer conductor of inner radius b. Determine the inductance per unit length of the line.
Homework Equations
the book states the methodology to find the inductance as follows:
1)...
Homework Statement
Consider a two-layered cylindrical wire with inner-layer permeability μ1 and outer-layer permeability μ2. A line current I runs through the center in the z direction. Calculate the bound currents and the magnetic field produced by the bound currents.
Homework Equations
[1]...
Homework Statement
[/B]
Two long, coaxial metal cylinders are separated by a material of conductivity sigma and dielectric constant epsilon. The radius of the inner cylinder is a, the radius of outer cylinder is b, and the length of both is L.
Suppose that the inner conductor is held at a...
Homework Statement .
Trying to find the potential between a variable capacitor that is made up of two coaxial cylinders of radii a and b, with (b-a) << a, when inner cylinder displaced by a distance y along axis.
2. Homework Equations
E = λ / 2piε0r
V = λ/2piε0 * ln(b/a) when there is...
Homework Statement
I have attached the problem
Homework Equations
E*A = Qenc/ E0
The Attempt at a Solution
At the moment I am looking at the problem more conceptually and seeing what is happening at each point and I wanted to know If I was on the right track.
r<a
As all charge would...
Let's say we have a coaxial cable with a 2d rectangular surface lying between the inner and outer conductors and running the length of the cable. I'm trying to understand why the magnetic flux through this surface only includes the magnetic field generated by the current flowing through the...
Homework Statement
I have posted the given question and conditions in the attached image
Homework Equations
(Q_enclosed/ epsilon_0) = closed integral (E-field) dA
Q_encolsed = p*A
V(r)= -Int_(from origin to r) (E-field(r'))*dl'
The Attempt at a Solution
[/B]
a)
E=0------>For r<a...
Hi Guys!
I'm doing a conceptual performance calculation and analysis on co-axial rotor UAV helicopter on hover. However, I'm having conflicting results and if anyone can help me, it would be very great.
The design constant of the helicopter are as follows:
MTOW = 20 kg
κ = 1.15 (Induced Power...
Every physics books show that wave prograpation in coxial cable is TEM wave, like in the picture. But we know that J=σ E from ohms law, which says current in same direction with E field, which is not the case here. What do you think the reason is ?
I was going through a worked example in book "Concepts in Thermal Physics" by S.J. Blundell and K.M.Blundell. The example talks about measuring viscosity of a gas between two coaxial cylinders.
Homework Statement
Two vertical coaxial cylinders. Outer cylinders is rotated by a motor at constant...
Hello.
I'm using coaxial cable to transfer power to the load with original aim that radiation from the coax would be low or almost nothing as current on both conductor (central conductor and outer shield layer - ground) are equal in amplitude and opposite in phase so their sum is zero; zero...
Homework Statement
A coaxial cable consists of two concentric cylindrical conductors as shown here: http://puu.sh/luFZx/7f3e1ccb07.png . The inner cylinder has a linear charge density of +λ1, meaning that each meter of the cable will have λ C of charge on the inner cylinder. The outer cylinder...
We have a coaxial cable with inner radius a and outer radius b. The coaxial cable is modeled as two very long circular metal cylinders. I'm supposed to calculate the electric field E, the electric potential V and the charge enclosed Q when a voltage is applied between the metal cylinder...
Hello, I would like to calculate the current distribution in a coaxial cable where the skin effect is significant. I asked this question on stackexchange and I provided pictures and more details there...
Hello. I have DC going through a coaxial cable, and I have calculated the E fields of the two dielectrics in between to be E_1 and E_2 with help of their D-vectors. The dielectrics are cylindrically shaped like the conductors. As in, one is in contact with the inner conductor, and one is in...
Homework Statement
http://postimg.org/image/vzhqi8er5/
Homework EquationsThe Attempt at a Solution
I understand all the calculations here - http://www.physicspages.com/2012/10/18/coaxial-cable-with-dielectric/
I have one issue that is bugging me though - if λ charge density is distributed over...