When I try to do Gauss, the permeability is not always that of the free space, but it varies: up to a certain radius it is that of the void and then it is the relative one. How can I relate them? I'm trying to calculate the capacity of a spherical capacitor.
The scheme looks like this: inside I...
The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from...
I am trying to simulate a Thick-GEM detector in Garfield++. In order to do so, I need information of the field maps which I generate using COMSOL. I've already extracted the mesh data and the potential data. For the initialise function, I need another file that gives dielectric information of...
Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}.
Determine the E-field inside and outside the...
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so in the 2nd page,when the dielectric material is introduced the gauss's law becomes $$\oint _ { S } \vec { E } \cdot \vec { d S } = \frac { ( q - q _ { i } ) } { \epsilon _ { 0 } }$$.But my question is why the ##{ \epsilon _ { 0 } }## is in the equation.Shouldn't...
Hello, the problem is better illustrated at the picture below.
The capacitor is isolated, with an initial charge Q0. I understand that Q0 does not distribute along the plates homogeneously. How could it be solved with the equivalent parallel circuit?
I) For the first part I used:
##V = - \int E ds = \int_a^c \frac{1}{4\pi\epsilon_0} Q /r^2 dr+ \int_c^{c+d} \frac{1}{k} \frac{1}{4\pi\epsilon_0} Q /r^2 dr + \int_{c+d}^b \frac{1}{4\pi\epsilon_0} Q /r^2 dr ##
And by using ##C = Q/V## We get an answer which is somehow large for writing here...
I read in various sources (such as page 8 of these notes) that the dielectric permittivity tensor of a lossless medium is always symmetric. I am wondering how this can be the case, when:
Phase accumulation in the medium could in theory depend on direction
Coordinate system may be rotated to...
Hi
I was reading about capacitors and potential energy. But the equation seems counter to how i thought.
For potential energy you have:
U = Q^2 / 2C
or
U = CV^2 / 2
But doesn't this suggest you lose potential energy the more capacitance you have? Since in the first equation as C increases U...
Homework Statement
A laser tweezer is a laboratory instrument, which uses highly focused laser beams to ‘trap’, hold or move small sized objects. The principle of the operation is that in the focal spot, the light intensity is inhomogeneous, and acts on the particle with a force that points...
I am studying about dielectric materials and their relaxation properties. There are several ranges of electromagnetic frequencies where different material show different kinds of resonance starting from molecular to atomic motions. Based on the frequency dependence of the imaginary part of the...
Say there are two parallel plates separated by a small fixed distance d and charged +q, -q. The force attracting the plates is F. If a solid block of dielectric (dielectric constant k) is introduced between the plates, will the force of attraction be different from F.
My answer: The electric...
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...
I have a fundamental question about the antennas made by using dielectric materials that I have not found a satisfied answer online. According to Wikipedia, antennas are described as,
"In radio, an antenna is the interface between radio waves propagating through space and electric currents...
I'm looking to see how much the dielectric constant of air will change mostly as a function or air temperature.
Is there a formula that outputs air dielectric as a function of temperature or atmospheric pressure?
Homework Statement
Having a conducting sphere with radius ##R## and charge ##Q##, dielectric is put on it so that a spherical shell with inner radius ##R## and outer radius ##3R## is formed. Calculate:
1. Electric permitivitty ##\epsilon## such that ##E(r), R<r<3R## is constant and there's...
Homework Statement
Consider a conducting sphere with radius ##R## connected to a voltage source of ##V_0## volts. If the sphere is then covered by a dielectric spherical layer of radius ##9R## calculated the relative permitivitty ##\varepsilon_0## needed so that the field in the empty zone...
If given a capacitor with stored charge, would its charge remain constant before and after it is immersed in a liquid (i.e. distilled water)? Why?
I know that before immersion, the capacitance would be = (ɛAV/d), but would that be the same if immerged in distilled water?
To my knowledge, CPP means cast-polypropylene, which I've seen used in a coaxial cable. Some cables use CPP as dielectric material. My question is:
1. what is the difference between PP(polypropylene) and CPP?
2. How is CPP made?
3. Is the permittivity and loss tangent of CPP different from that...
Homework Statement
I have an infinitely long cylinder of a dielectric material, surrounded by another dielectric material and coated with graphene which has surface conductivity \sigma, implying it has a superficial current. The sheet of graphene is very thin, and the dielectrics are asumed to...
Homework Statement
I'm trying to do all the calculations for the attached paper, and I'm having trouble with the boundary conditions for P polarization. My question is, how can I arrive to those conditions? The problem is 2D, an infinite dielectric cylinder coated with a layer of graphene...
consider that we have two dielectrics inside a capacitor as shown in the picture, let0s consider also that Q is the charge of the capacitor and d the distance between the two plates , the first dielectric occupy a surface of S/3 with a dielectric constant of er1 and the second a surface of 2S/3...
Here is the experience: I put two electrodes inside paraffin oil (separated by at least 3cm), and submitted the electrodes to high voltage. At 20000 V - 30000 V, strong streams can be observed inside the paraffin oil. Since paraffin oil is a good dielectric, I just would like to understand the...
Homework Statement
Consider an infinite environment with electrical permittivity non-homogeneous $$\epsilon=\epsilon_0(1+a/r)$$ a being a positive constant. A conducting sphere of radius R and charge Q is put on that environment, centered at r=0. Determine the electric field $$E$$, the...
Homework Statement
With regards to a one dimensional conducting wire with a homogeneous charge density λ surrounded by a cylindrical glass dielectric of radius R, find:
(a). The displacement vector inside the dielectric
(b). The surface bound charges on the surface of the dielectric
Sorry...
Q) A conducting sphere of radius R floats half submerged in a liquid dielectric medium of permittivity e1. The region above the liquid is a gas of permittivity e2. The total free charge on the sphere is Q. Find a radial inverse-square electric field satisfying all boundary conditions and...
I know that mie theory is used to analyze the absorption/scattering/extinction of a homogeneous sphere within a homogeneous dielectric medium. However, if I wanted to perform the same analysis on a sphere enclosed by two different media, is there an analytic solution to this?
Homework Statement
I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle.
https://ibb.co/b0W4BQ
Homework Equations
∫D⋅ds=Q
D=E+γP
C=Q/V
The Attempt at a Solution
Suppose the top plate has a positive charge...