What is Charge: Definition and 1000 Discussions

TL;DR Summary: Find the electric field of a long line charge at a radial distance where the potential is 24V higher than at a radial distance r_1=3m where E=4V/m. Answer: 29.5V/m. Never mind: I retract this question. The integral apparently is supposed to diverge! I apologize for not reading...

I think I read somewhere that the trajectories of particles in the De Broglie–Bohm theory do not cross, is that true? If true, then in the case of Rutherford scattering the trajectories below can't be those of the De Broglie-Bohm theory? Thanks.

Doing so, we can consider the balloon to be a point charge (approximately). Can we do it in this case, when there are only electrons on its surface? Or is it stupid and we can't do it under any circumstances?

I know we're supposed to attempt a solution but I'm honestly super confused here. I think the second an third terms of the del equation can be cancelled out because there is only an E field in the r hat direction, so no e field in the theta and phi directions. That leaves us with ##\nabla \cdot...

If conservation of charge gets violated in future experiments, what would be the implications on relativity? I have some faint idea that this will cause photons to have non-zero rest mass, but does this affect special relativity at all? Also, does special relativity make conservation of charge...

Hi! For this problem, The solution is, However, why did they not include constants of integration in their working shown in red? Many thanks!

Why do we have a charge in the denominator of equations for voltage and el. potential if both voltage and el. potential are not dependent on charge? Is it just because that was the only way to derive the formula for voltage and then we realized we don't need q? U=W/q --> U=eqd/q.

I wonder how it is possible that a positive charge can exert el. field beyond negative charge? Shouldn't they "connect" and therefore positive charge should stop to have el. field beyond neg. charge? I mean, I am obviously wrong about that, but can someone please explain why/how el. field from...

I drew a diagram using all of the information however, I am stuck and not to sure how to get one of the charges

How and why can charge be evenly or uniformly distributed in a conductor? How can such near perfect configuration of charge be achieved? Is outside influence (or force) or any special scientific tools or instruments required to accomplish that? By definition, electrostatic equilibrium is...

How can we detect electrical effect of a static point charge at all? I think of a point charge like a sea urchin. With field lines going outwards in all directions (for +ve). So the vector pointing at me directly should be canceled perfectly by the vector going away from me. And so each line...

Part (a) was simple, after applying $$Q=\int_{\mathbb{R}^3}^{}\rho \, d^3\mathbf{r}$$ I found that the total charge of the configuration was zero. Part (b) is where the difficulties arise for me. I applied $$V(\mathbf{r})=\frac{1}{4\pi \epsilon _0}\int_{\Gamma }^{}\frac{\rho...

hello i would like to understand something, i found the right answer but there is still something i don't understand. here is the figure and here is my correct solution what i don't understand is why F(3,Q) is 3kQ/r^2 i mean why is the 3? i only calculat the force between q3 and Q so why...

Wak a ball with a bat and the ball accelerates. Now under gravity, hold the ball out horizontally, let go and the ball accelerates ... without a wak. Given that gravity arises from curved space-time, I suggest further that the acceleration of the ball arises when sub-atomic particles (in the...

I've attached what I have so far. Used Gauss's law, everything seemed to make sense except the units don't work out in the end. The charge density function if given by: r(z)=az, where z is the perpendicular distance inside the plane.

I put the net charge density ##\rho_q = e\delta## so that ##\nabla \cdot \mathbf{E} = e\delta / \epsilon_0##, then I tried Maxwell IV:\begin{align*} \dot{\mathbf{E}} + c^2 \mu_0 \mathbf{J} &= 0 \overset{\mathrm{div}}{\implies} e\dot{\delta} + \nabla \cdot \mathbf{J} = 0 \end{align*}but this...

I hope you all have a wonderful day, Some time ago, I bought a device that is supposed to eliminate static charge on my vinyl records (which aids to the overall sound quality). I was sitting on the couch and having a deep thought, as me myself have no professional background in physics, I...

I do not mean neutral electrical charge, but a forth kind (if exists) I am in 9th grade, and someone asked the teacher if there is an electrical charge that is not positive, not negative and not neutral, maybe something in the middle of them. The teacher said that there is a charge like that...

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...

Total number of charges = charge per ion * number of ions = 1.6*10^-19 * number of combined ions Solution: 1.6* 10^-19 * number of negative ions

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...

In Purcell's E&M Section5.3 "Measurement of charge in motion", he said when a charge is in motion, the force on test charges may not be in the direction of radius vector r. And in next paragraph, he defined Q by averaging over all directions. However, he just measured the radial component of...

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...