Charge Definition and 1000 Threads

Hello everyone, This is in reference to fig 5.19 (screen shot attached - please read the paragraph which says "Figure 5.19 shows the..."). I don't get why the field outside of the sphere of radius ct acts as though the particle would have continued its motion. Author's words : "The field...

According to Helmholtz’s theorem, if electric charge density goes to to zero as r goes to infinity faster than 1/r^2 I'm able to construct an electrostatic potential function using the usual integral over the source, yet I don't understand how this applies to a chunk of charge in some region of...

What I have done: The electromotive force due to Faraday's Law is: ##\mathcal{E}=-\frac{d\phi(\vec{B})}{dt}=\frac{d}{dt}(Ba^2)=a^2\frac{dB}{dt}=-10^{-4}V.## In the circuit, going around the loop in a clockwise fashion: ##\oint_{\Gamma}\vec{E}\cdot d\vec{l}=-\frac{d\phi(\vec{B})}{dt}\Rightarrow...

I could try to apply the Liénard-WIechert equations immediatally, but i am not sure if i understand it appropriately, so i tried to find by myself, and would like to know if you agree with me. When the information arrives in ##P##, the particle will be at ##r##, such that this condition need to...

I have tried to solve the problem by setting as a condition that the electric field inside the conductor has to be 0, but in this way I have two unknowns (σ1 and σ2):

Potential of a moving point charge is given as ##V (\mathbf r,t)= \frac{1}{4\pi\epsilon_0}\int \frac{\rho (\mathbf r',t_r) }{|\mathbf{ (r-r')}|}d\tau'## Griffiths says: " It is true that for a point source the denominator ## |\mathbf{(r-r')}|## comes outside the integral..."Why does it come...

I understand part (a) of this question, and my answer for that part is: *For r < a* E = (ρ0 * r4) / (6 * ε0 * a3) * For r ≥ a* E = (ρ0 * a3) / (6 * ε0 * r2) Now, for part (b), I understand one solution is, for r < a, find the work done to bring a point charge q from infinity to a and then from...

With a capacitor with a dielectric with the battery on, ##E_{total} = E_0 + E_i## ##\frac{Q_t}{dC_t} = \frac{Q_0}{dC_0} + \frac{Q_i}{dC_i}## thus, ##\frac{Q_t}{C_t} = \frac{Q_0}{C_0} + \frac{Q_i}{C_i}## since in a battery ##V_t = V_0, V_i = 0##, so either ##Q_i = 0## or ##C_i = infinite## but...

I am confused why we don't take into account the lids of the cylinder since the Gaussian cylinder is of finite height L as shown in the image

Hi everyone! I'm pretty new in this forum, I found the topics here very relevant to my physics course. And here is my question: Given the following drawing, two infinite sheets (in y and z axis) of ideal conductive material. their thickness is infinitesimal (dx->0). The electric field is...

If we put a positive charge outside of a conductor, there is an induced charge, but if we put a positive and negative charge inside a conductor, there is no induced charge?

Homework Statement:: This isn't a homework question but just a theoretical questions. [mentor’s note: moved to a more appropriate forum for theoretical questions.] I know that current is defined as the rate of change of charge per unit time. i = dq/dt This makes sense for a capacitor which...

Hi , I'd like a little bit of clarification about Section 2.6 from Jackson's classic book on E & M. Section 2.6 starts out with the problem of a "conducting sphere" near a point charge, but then it confusingly veers away to a problem where potential is prescribed to vary with azimuth and polar...

The book gives an answer of Q = 3.2 x 10^-19C I get an answer of 6.67 x 10^-19C. Workings below:

Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below? However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an...

It's not a homework. I came up with this problem myself. Trying to understand fundamentals of electronics. Do you know how to solve it? Is voltage somehow related to electron energy levels? What knowledge should I gain to be able to solve problems like that? Thank you! If we ground the cathode...

If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...

$$\phi_E=\dfrac{Q_{\textrm{enclosed}}}{\varepsilon_0}\Rightarrow Q_{\textrm{enclosed}}=9,6\cdot 10^{-7}\, \textrm{C}$$ $$Q_{\textrm{enclosed}}=\sigma S=\sigma \pi R^2\Rightarrow \sigma =\dfrac{Q_{\textrm{enclosed}}}{\pi (0,1^2)}=3,04\cdot 10^{-5}\, \textrm{C}/\textrm{m}^2$$ I have a lot of...

Hello! I am trying to solve this exercise of the electric field, but it comes out changed sign and I don't know why. Statement: On a straight line of length ##L=60\, \textrm{cm}## a charge ##Q=3,0\, \mu \textrm{C}## is uniformly distributed. Calculate the force this linear distribution makes...

Hey, I have a really short question about electrostatics. The boundary conditions are : \mathbf{E}^{\perp }_{above} - \mathbf{E}^{\perp}_{below} = -\frac{\sigma}{\varepsilon_{0}}\mathbf{\hat{n}} , \mathbf{E}^{\parallel }_{above} = \mathbf{E}^{\parallel}_{below}. My question is what is...

Disclaimer: This is not a repost. The problem wants me to calculate the force of a p.c. , that is isolated by itself (this p.c. is the only charge this problem starts with in this problem) inside a capacitor, a distance h/4 from the bottom plate. This is what I have though of so far but I...

For (a) this problem, the only thing I can see changing is the distribution of the negative charge on the inner wall of the cavity. When the point charge is in the center of the cavity, you could say the induced charged is spread symmetrically on the inner cavity wall in order to oppose the...

Consider a simple DC circuit containing a 9V battery, a switch, a 10 kΩ resister and a 100 μF capacitor all in series. When the switch is thrown, it will take basically 5 seconds for the capacitor to reach full charge. Based on what I have read online, the charge on the above capacitor is...

I believe I have all parameters set up correctly to evaluate part A of this problem but I am unsure of the bounds. I can't integrate from 0 to R because that part of this sheet has a hole there. I need to integrate from R to the other end of the sheet. Im not sure how I would figure out the...

I am confused because I thought this was a method of charging a conductor. Why would the system be reaching a state of equilibrium?

By measuring angle \theta from the positive ##x## axis counterclockwise as usual, I get ##d\vec{E}=k( (\lambda_2-\lambda_1)\cos(\theta)d\theta, (\lambda_2-\lambda_1)\sin(\theta)d\theta )## and by integrating from ##\theta=0## to ##\theta=\frac{\pi}{2}## I get...

Hi, I have a dialectric cube and inside the center of the cube I have a part where we have Introduced evenly electrons. I have to find the polarization charge density in the 3 regions. I know outside the cube is the vacuum, thus ##\vec{P} = 0## and inside the dialectric (non charged part)...

In this question it is given that the sphere which is conducting is initially given a charge q then due to nonuniform mechanical strength and due to electrostatic force it creates a Small hemispherical bulge on its surface? okay my doubt is Let me define a term σ where σ is surface density...

I'm a bit confused about what difference there is (if any) between charge and force carriers. I imagine charge as a field around a particle that pushes or attracts other particles. But we're also told that bosons mediate the forces by exchanging. So there seems to be a redundancy unless charge...

The electric field is the one generated by the charge ##+Q## on the inner sphere of the capacitor, which generates a radial electric field ##\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}## which, due to the presence of the dielectric, become...

Gauss' law: $$\iint_{\partial A}\vec E\cdot d\vec A=\frac{Q}{\epsilon_0}$$ Suppose we have a unevenly charged non-conducting spherical shell, in which a Gaussian surface is placed. In this case, is the electrical field on A 0, given that there is no charge inside A? I came up with this example...

Whats shielding effect and effective nuclear charge?

In the Reissner–Nordström metric, the charge ##Q## of the central body enters only as its square ##Q^2##. The same is true for the Kerr-Schild form. This would seem to imply that all effects are even functions of ##Q##. For example, the gravitational time dilation is often written as $$\gamma =...

Hi all, I was trying to understand an equation where: axial charge, ##G_A=g^P_A(Z_+-Z_-)+ g^N_A(N_+-N_-)## What is the meaning of ##Z_+## , ##Z_-##, ##N_+## and ##N_-##? From the article I read, axial charge will be zero when the nuclei has zero spin. What if I have Germanium 73 which has...

Suppose I have a perfect crystal(e.g.TiO2-Rutile, band gap=3ev), under UV light, there should photoconductivity, according to the condensed matter theory, some of these excited conduction band electrons would form small polarons, I am wondering how many percent of the free conduction band...

I am having some problems involving the force that a source moving with speed v along the x-axis would exert on a test charge at the x axis. Moving to the frame of the source charge, we got that the electric field it exerts is $$E' = kq/x'²$$ Now, moving back to the lab frame, and considering...

I'm new to Astrophysics and I'm just now learning about Antimatter-Matter asymmetry. I understand some of the theories involving how this imbalance couldve occurred, but I'm confused on why the net charge of the universe stayed at zero. It seems to me like if the antimatter particle changed to a...

There are some question involving the statement. One of them is about the charge density in S' frame. It asks to calc it. I thought that i could calculate the electric field in the referencial frame S' and, then, use the formula $$ E = \lambda / 2 \pi \epsilon l $$ In that way, i would obtain...

Hi! Given three voltages as follows; Q1 = 1C,Q2 = 1C,Q3 = 2C The distance a is 1m and b = 2m a) Find the values of the forces that are acting on Q2 I did that like this; $$ F_{12} = \frac{Q1*Q2}{4\pi\epsilon r^2} $$ $$ F_{32} = \frac{Q1*Q3}{4\pi\epsilon r^2} $$ The results are ...

Picture: Energy source => LR Oscillator => Transformer => Transmission line => Electric dipole antenna => traveling wave Why would the charge even oscillate in the antenna as opposed to building up in the antenna? The transmission line + antenna is not a closed circuit right?

hi guys our professor asked us to confirm the units of volume charge density ρ and also the surface charge density σ of a dielectric material given by $$ \rho = \frac{-1}{4\pi k} \vec{E}\cdot\;grad(k) $$ $$ \sigma= \frac{-(k-1)}{4\pi} \vec{E_{1}}\cdot\;\vec{n} $$ I am somehow confused about the...

Question: Here's my attempt with the relevant equations: The correct answer is F = -99.4 az μN. Could someone please figure out my mistake?

Hi everyone. I am an engineer by trade (don’t hold that against me!) but I was trying an experiment for the latest of my crazy inventions and am missing some key logic in static electricity which I was hoping you could identify. Equipment 1. Wimshurst machine (like...

Question: Relevant Equations: My attempt: Could someone please confirm my solution?

A known result is that the average field inside a sphere due to all the charges inside the sphere itself is proportional to the dipole momentum of the charge distribution (see, for example, here). I wonder whether the same result can be applied in the case of a spherical shell of non-uniform...

I think that it is a trick question and that the answer is that given dependence does not exist. Could anyone tell me if I am right?

I am a little lost on the last step of this problem. I get that we want to know how much time elapses for the capacitor to reach 2/3 of its final charge. That is why 2/3Qf is equal to Qf(1-e^-t/RC). I don't understand how we make the jump to e^-t/Tau is equal to 1/3? and then somehow e^-t/Tau...

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...

I have already calculated the polarisation that is $$ \mathbf{P} = \frac{\rho_f r}{2} \left( 1 - \frac{\epsilon_0}{\epsilon} \right) \hat{r} . $$ I tried to use the following formulas to calculate the density bound charges. For the surface bound charge I got: $$ \sigma_{b1} = \mathbf{P} \cdot...

The charge associated with gravitational interactions is the mass. In the Standard Model, charge conjugation is the "flippin" of all kinds of charges (electric, color, etc). So, if we were to, say, incorporate quantum gravity in a beyond the Standard Model theory, what would the full charge...