Dielectrics Definition and 154 Threads

Dear Forum, I would like to ask, if a certain construction is possible: I have something like coaxial cable, but instead of a conductor at the core I have a different dielectric. Now I want the resonance outside the core to still happen, but not inside the core. Is this possible? Because I...

my sir gave us the above question as homeork,our task to derive why it happens so I couldnt get it right. So today he gave the answer to it. we were also a..sked to find the induced charges on the dielectric surface. . E ext : electric field between capacitor plates when no dielectric was put E...

Its form is: (n2-1)/(n2+2)=(4π/3)Nam There is one simple problem with it. Rearrange the left side and you get: (n2+2-3)/(n2+2)=(4π/3)Nam 1-(3/(n2+2))=(4π/3)Nam As you see, the left side cannot reach unity for arbitrarily large n2. But there is no reason why N cannot be arbitrarily large! How...

I think definition (a) is not correct since the center of charge distribution rather than mass distribution is important here. The correct definition is the one given in (b). I am thinking that a distribution of charge will have a center of charge ##(x_c,y_c,z_c)## for -ve charges according to...

It is believed that Maxwell equations (together with other relations depending on the materials) are sufficient to account for any electromagnetic macroscopic effect. The problem is that, for a Maxwell equation to hold, it must at least be defined. Consider for example the case of two...

Hello PhysicsForums community, I have been reading through Zangwill's Modern Electrodynamics all on my own, and I've just joined here hoping I can post some questions that come up for me. To start, I am confused about something in section 6.7.1, concerning the variation of total energy U of a...

I considered the capacitor as two capacitors in parallel, so the total capacitance is ##C=C_1+C_2=\frac{\varepsilon_0\varepsilon_1 (A/2)}{d}+\frac{\varepsilon_0\varepsilon_2 (A/2)}{d}=\frac{\varepsilon_0 A}{2d}(\varepsilon_1+\varepsilon_2).## Since the parallel component of the electric field...

The force on charge ##q_2## will depend on the electric field in medium with dielectric ##K_2##. Electric field in this second dielectric due to ##q_1## is ##E = \dfrac {kq_1} {K_2r^2}## where r would be the distance from ##q_1##. So, the electric field at the point where charge ##q_2## is...

In the 7th edition of the book "Elements of Electromagnetics by Matthew N. O. Sadiku" On page 190 the author goes on to say: "We now consider the case in which the dielectric region contains free charge. If ##\rho_v## is the volume density of free charge, the total volume charge density...

The geometry of the capacitor can be either cylindrical or spherical.

We have a material of dielectric constant (or relative permittivity) k=##\epsilon_r##. I place it in an external uniform electric field pointing down ##E_0(-\hat z)##. Induced charges and net field There will be charges induced on the near and far surfaces normal to the field (top one...

If we have a small dielectric sphere and a point charge, they will experience an attractive force due to electrostatic induction. (From the elongation/rotation of charges bound to individual atoms). Likewise, if we have a small metallic sphere and a point charge, they will experience an...

Could somebody check my solution?

Hi, so the four-dimensional generalization of $$\vec{B}=\mu\vec{H}$$ is $$F_{\lambda \mu}u_{\nu} + F_{\mu \nu}u_{\lambda} + F_{\nu \lambda}u_{\mu} = \mu (H_{\lambda \mu}u_{\nu} + H_{\mu \nu}u_{\lambda} + H_{\nu \lambda}u_{\mu})$$ From these four-tensors and four-vector I should be able to...

When placed in an electric field, a conductor has induced charges and a dielectric has bound charges. When there's no net bound charge density in the bulk of the dielectric, bound charges stay on the surface only, like induced charges in conductors. In Maxwell's eqs, the induced charges are...

This is the problem I'm working on. So far I know: 1. I am assuming the free charge density is +sigma for the top plate and -sigma for the bottom plate. 2. The electric field from the plates goes from top to bottom plate, in the negative z direction. 3. The electric field of the capacitors...

During the derivation of the dielectric function of a plasma (Kittel 8. ed. chap. 14), this somewhat mysterious quantity ε(∞) is inserted to account for the high-frequency dielectric contribution of the ionic background. In some ways, I see how this is related to the "external" charge density in...

Hello, I am reviewing how classical EM problems are treated when dielectric materials are involved. Maxwell's equations relate the following vector fields: ##E(r,t)##, ##B(r,t)##, ##D(r,t)##, ##H(r,t)##, ##J(r,t)## and scalar field ##\rho(r,t)##. The two constitutive equations are also needed to...

From what I could understand, without external perturbation the nucleus and its cloud of electrons are in an energetic balance. Nevertheless, when they are put in an electric field, the nucleus moves in its direction and the cloud in the opposite. Now, this electric field apart from a torsion...

[PAGE 1] [PAGE 2] [PAGE 3] 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...

Hi, I would like to know how to calculate the total capacitance for a capacitor that has a certain plate overlap area and two dielectrics in between, one being a solid state dielectric and the other one being air. This is not a school project, I just thought about it and tried to calculate...

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?

Homework Statement Consider the following system: which consists of a conducting sphere with free charge , a dielectric shell with permittivity ##\epsilon_1##, another dielectric shell with permittivity ##\epsilon_2## and finally a conducting spherical shell with no free charge. Homework...

Homework Statement A parallel plate capacitor has area A = 1 cm2 and a plate separation of d = 0.01m (1cm). Water at room temp (20°C) is poured into a mica cylinder and placed between the plates filling the volume of 1cm3. Find the Maximum capacitance, voltage and charge for the capacitor as...

1. The problem statement, all variables, and given/known data A parallel-plate capacitor has the space between the plates filled with to slabs of dielectric, one with constant K1, & one constant K2. each slab has thickness d⁄2, where d is plate separation, show the capacitance is? Homework...

Hi, I am trying to understand capacitors and have come across the example in the attached image. What I would like to understand is how to calculate the electric field at some distance x within the capacitor. With x>>R , x<R and x=R . The image is of two circular disks as the...

Homework Statement a) State the boundary conditions for the electric field strength E and electric flux density D at a planar interface separating two media with dielectric constants ε1 and ε2. b) A parallel plate capacitor with a plate separation d is filled with two layers of different...

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...

Homework Statement A capacitor has square plates of length a separated at a distance d. Dielectrics are inserted as shown in the figure. Find the capacitance Homework EquationsThe Attempt at a Solution [/B] I know that I have to integrate, but can't get an expression

How do dielectrics affect the number of modes for standing electromagnetic waves in a box?

Forces on dielectrics I found difficulty in understanding this topic from Griffith. Here, while calculating F, in eqn. 4.61 , Griffith doesn't bother about energy stored in fringing field. So, even if I assume that there is no fringing field, then following the above procedure, I can say...

Can a sphere with a frozen - in uniform polarization ## \vec P ## be considered a linear dielectrics? Following the definition of dielectrics given in Griffiths: The electric field inside the sphere, ## \vec E = \frac {-P}{3 \epsilon_0} ## So, ## \vec P ≠ ε_0 χ_e \vec E ## as ## ε_0 χ_e##...

I am a Graduate student in Electrical Engineering. I have to work on Electromagnetic, Dielectric, Magnetic field and Polarization for my project. But my problem is I do not have a good background in this course. Now, I really need it in graduate level. My question is, can you guys introduce me a...

Hello there, I was wondering if anyone wouldn't mind helping clarify what is occurring with a charged capacitor for me. I understand that in a charged capacitor one conducting plate is negatively charged and one is positively charged due to the distribution or rearrangement of electrons. There...

Homework Statement Hi guys, I hope you can help me with this problem, because I do not have any idea and I could not find anything that could help me, thank you in advance! Draw the electric field lines due to a punctual charge Q immersed in a dielectric medium with constant K1. Q is separated...

Homework Statement Below are a few equations listed in my text for use in calculating capacitance in dielectrics. I'm wondering which of these are applicable in specific scenarios Homework Equations 1. k = C/C0 - with C0 indicating capacitance w/o dielectric 2. v = v0/k 3. E = E0/k 4. σi = σ(1...

Is the "Voltage variable capacitor" described in patent US 20070242410 A1 a commercially available component? Has anyone heard of this method of changing the dielectric constant using a biasing voltage? It has been nearly 13 years since the patent was filed, but I've never heard of it. It would...

Hello! Let's consider a plane wave represented by a ray, propagating in a 2D dielectric slab. It has a medium with refractive index n_1 as its core and a medium with refractive index n_2, n_2 < n_1, as its cladding. In order for this ray to represent a mode, it must satisfy two conditions: -...

Homework Statement The question is attached. Homework Equations The Attempt at a Solution I understand that the question would return to a typical conductor problem when ε2 >> ε1 so for the quadrant one, I placed image charges of q_1 at (d1 , 0 , -d2), -q1 at (-d1 , 0 , -d2) and another q1 at...

Homework Statement A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities ( ε1=2 and ε2=4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. the ratio...

Homework Statement Two parallel plates are connected to a battery which maintains a constant potential difference of 12.0 V. The distance between the plates can be varied and there are three plates of different dielectric materials available: rubber (0.40 mm, κ = 6.7), glass (4 mm, κ = 7) and...

Homework Statement Consider the situation shown in the figure. The width of each plate is b. the capacitor plates are rigidly clamped in the lab and connected to a battery of emf E. All surfaces are frictionless. Calculate the value of M for which the dielectric will stay in equilibrium...

Homework Statement I'm having a problem using the fresnel formulae for these two problems below: 1. Using Fresnel formulae and expression for the Poynting vector show that at the interface between two dielectrics in the absence of absorption R+T=1, where R – is reflectivity and T –...

A typical mode in a dielectric slab like this, with propagation along x, uniformity along z and refractive index variation along y, is represented by the following function: f (y) = \begin{cases} \displaystyle \frac{\cos (k_1 y)}{\cos (k_1 d)} && |y| \leq d \\ e^{-j k_2 (y - d)} && |y| \geq d...

Homework Statement The parallel Plates of a capacitor have an area of 2.00 x 10-1m2 a separation distance of 1.00 X 10-2 m and are connected to a 3000 V power supply. The capacitor is then connected from the supply, and a dielectric is inserted between the plates. We find that the potential...

Homework Statement A spherical capacitor consists of two concentric spherical conductors of radii ##R_{1}## and ##R_2, (R_2 > R_1)##. The space between the two conductors is filled with a linear inhomogeneous dielectric whose relative permittivity varies with the distance ##r## from the...

Hello! This post is strictly related to my previous one. Let's consider the same context and the same image. Regarding the oblique incidence of a wave upon an interface between two dielectric, all the texts and all the lectures write an equation like the following: e^{-j k_1 y \sin \theta_i} +...

Homework Statement The space between 2 perfect conductor plates parallel to the x-z plane separated by a distance 2a are filled with 2 dielectric materials whose surface also lies in the x-z plane, at a distance equal to a from the plates. We're looking for TM modes propagating along the z...

At the moment we are working through problems in Griffiths' Electrodynamics textbook and it got me thinking... In magnetostatics we have the magnetic vector potential A and in the use of dielectrics problems we have the vector D. Why is it advantageous to use these vectors and not just stick to...