Charge Definition and 1000 Threads

Let us say we have a cavity inside a conductor. We then sprinkle some charge with density ##\rho(x,y,z)## inside this surface. We have two equations for the electric field $$\nabla\times\mathbf{E}=0$$ $$\nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}$$ We also have the boundary conditions...

I couldn't solve the question. Can you help me?

I've been discussing Newton's Shell Theorem re: gravity with someone, and thought of the analogy to charge. 1. I think the net effect on a negative charge inside a hollow sphere of positive charge will be zero. i.e. No net attraction. Yes? 2. But what would happen to the magnetic field if the...

The problem is symmetric around the z axis, thus the force must be in the z direction only. I tried dividing both rings into differential elements, then integrating through the upper ring to get the z component of the total force on the upper ring due to a differential element of the lower ring...

I quite understand the fact the EPE (Electrical Potential Energy) of a system of two charges are U = k*qQ/r, Q is fix. however when it comes to three charges i get lost. because my reasoning is : if q1 is fix then the EPE of the system when q2 is brought is U2 = k*q1*q2/r12, when q3 is brought...

Electric potential energy at initial: Ee=kq1q2/r =(9 ×10 ^9×1.5×10^-6×(-5)×10^-6)/0.1 =-0.675J Electric potential energy at the closer point: Ee=kq1q2/r =(9 ×10^9×1.5×10^-6×(-5)×10^-6)/0.05 =-1.35J Δv=ΔEe/q =(-1.35+0.675)/1.5×10^-6 =4.5×10^5V or: Initial position...

Modern batteries use double-sided anode and cathodes for greater energy density. Series wiring of batteries is typically accomplished by connecting the anode of one cell to the cathode of another. However, can series be accomplished by stacking double-sided anode and cathode alternatingly with...

All the references I find refer to safely charging lithium cells by a method like this: https://www.powerstream.com/li.htm The next page shows the effects on capacity of charging to less than the 4.2 V terminal cell voltage. For example, charging to 4.0 V still provides 73% of the capacity...

Hope someone can help!

All are used to finding the image charge induced by a source charge outside a conducting sphere. The solution is supposed to also work for the case where the source charge is inside the conducting sphere, in which case the sphere is now a conducting cavity. But the solution suggests the image...

hello Witch of these are certain sentences? a-\dfrac{e}{m_e}>\dfrac{H^{-}}{m_{H^{-}}}\cdot{1000} b-\dfrac{e}{m_e}>\dfrac{H^{+}}{m_{H^{+}}}\cdot{1000} The first accurate measurement of e/m was made by english physicist J.J. Thomson in 1897, who demostrated that the quotient charge-mass of the...

I have already calculated full charge inside the sphere: e = ∫ρ dV = 2πBr^2 And I know that electric potential on the edge of the sphere is: U = e/ 4πεr The idea is that I calculate work by the change of electric potential energy, but to do that, I have to calculate electric potential energy in...

I tried applying loop law but I am not really sure we don't really have a closed loop here. I guess they're testing some concept here that I'm not very good at (Why do i keep coming back to mutual inductance for some reason:|) Any help will be appreciated:)

Well i don't you to solve the question for me but I want you to clarify the concepts pertaining to this question. My question is how do I write a equation for the circuit since the there is same charge on one of the capacitors. While writing the equation should i put the voltage across the...

1. Can I use the surface charge equation: $$Q = \frac{Vk\epsilon_0A}{d}$$ Where V = Voltage, k = dielectric constant, ϵ0 = permittivity of free space , A = Area of plate and d = distance between plates. For a conductive plate within an electric field? My thinking is that if the plate is...

Please help. Thank you.

On p. 246 in the Peskin QFT textbook, below is stated where Z3 is defined as the residue of the q2 = 0 pole, explicitly as $$Z_3=\frac{1}{1-\Pi(0)}$$ and e is the bare charge. In advance, the exact photon two point function is calculated as $$\frac{-ig_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ Though...

I do not have the solutions to this problem so I'm wondering if my attempt is correct. My attempt at solution: We have two surfaces which we can calculate the area of. I think we can use gauss law to find the electric field and then integrate the E-field to find the electric potential. So for...

I am trying to calculate the interaction energy of two interpenetrating spheres of uniform charge density. Here is my work: First I want to calculate the electric potential of one sphere as following; $$\Phi(\mathbf{r})=\frac{1}{4 \pi \epsilon_{0}} \int...

When I asked "Can we transfer the whole charge of a body to another body?" my colleague replied: "If charged body (say 5 Coulomb) is any charged conductor ##A##, it can be done by enclosing ##A## completely by second uncharged conductor ##B## and connecting them by a conducting wire ##B## will...

Hello! Can someone point me towards some papers/readings providing formulas (derived theoretically or based on experimental data) for the nuclear charge radius? Almost all the papers where I found a formula for that are of the form ##aA^b+c##, where a, b and c are constants and A is the mass...

My first attempt at solving this was to calculate the induced charge in A by making ##V=0##: ##\frac{q_{A}}{4πεR_{1}}+\frac{q_{B}}{4πεR_{3}}=0## ##q_{A}=-q_{B}\frac{R_{1}}{R_{3}}## But that's not the answer. Any help is welcome!

It seems to me that one can obtain the required result by using just one neutral sphere and one ground wire. Let A be the charged sphere and B be the neutral one. Initially ##Q_A=Q## and ##Q_B=0##. put A and B in contact. As a result ##Q_A=Q/2## and ##Q_B=Q/2##. ground B, so that ##Q_B=0##...

The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of...

I'm just going to skip some of the step since I only need help with understanding the last part. After rearranging the equation stated at "Relevant equation" (and skipping some steps) we will get: E * 4*pi*e0*R^2 = integral pv * 4*pi*R^2 dR E = 1/(4*pi*e0*R^2) * 4*pi * integral pv*R^2 dR E =...

There must be something I'm not understanding about capacitors in series. I know that we can treat them as one equivalent capacitor with: (1) with 1/Ceq, (2) same Q as anyone of the capacitors, (3) and add up the Vs for the sum total V across them. If the equivalent capacitor (Ceq) would...

Hello guys! When talking about electrochemistry what is the difference between saying "electron transfer" and "vectorial electron transfer". It seems to me that "vectorial electron transfer" is just another fancy way of saying "electron transfer" but I am not quite sure if there is a kind of...

I was wondering if there is a way to deduce the solution of the potential of a charge outside a sphere given by the image method, though Green functions. Because of a Dirichlet condition (GD(R,r')=0), I know that a solution can be written as GD=Go+L, where ∇2L=0. But in order to approach this...

Merged thread deleted first post next post is the first post.

If they are equal and opposite, then wouldn't the net charge be zero? I don't know how else to reason this problem p = 0d or just 0

So is it becouse the material or becouse the fact that the balloon is the object that moves and the hair is static. and does every two objects that been grabed together will nacessrly continues each other. and also why does the minos of a bttary doesn't stick to the flower

Hi, I have a charge q1 = -10 * 10^9. The the coordinatesare (3,4)m. I found the electric field vector that is (-2160i -2880j) n/c. My questions is if I add a charge q2 to the the coordinates(0,0) is the electric field stay the same?

Hello So here is my question Not so sure how to approach this question This is what I have worked out so far which is the magnetic field strength of the solenoid, not sure if this comes in helpful though Thanks for any help!

The correct answer is B, but I am not sure why. I have a few confusions regarding this problem. First of all, I had thought that we cannot use Gauss' Law to determine the flux through a SIDE of a cube since Gauss' Law only works for SURFACES. How can we determine how an electric field pierces a...

The answer according to the key is C. I thought the answer would be E since the electric field inside a conductor is always zero. Can someone explain why the answer is C?

In my most recent post, I tried to investigate the V(r) verses “r” for several charge distributions on conductive paper. The discussion there made me realize that the common conductive paper activity is not suitable for doing that. Nevertheless, I am interested in doing projects where I can find...

I am needing clarification for a concept. I understand that electrons carry a negative charge and that protons carry a positive charge. I also understand that a plastic rod picks up electrons when I rub it with a piece of wool. From the conservation of charge, the piece of wool must have a...

"a charge smaller than e has not been found. if one determines the amount of charge on any charged body like a charged sphere or charged drop) or any charged particle (like positron, a-particle) or any ion, then its charge is always found to be an integral multiple of e, i.e., e,3e; 4e,... No...

I tried looking for the other charge using the equation k|q1||q2|/r^2 but it tells me that my answer is wrong

My answer was +Q/3. I was assuming that the charges would distributed themselves completely. But, apparently, I'm wrong? For example, if there were 12##e^-##s on Sphere C, then, in the first step in the system: the ##e^-##s would balance out until each sphere has 4 ##e^-##s each? What am I...

Firstly, I would like to check if I drew the diagram correctly: I'm unsure of the question's phrasing in this case. Should if the drawing is correct, (i) When radius is 1cm, charge enclosed = -10mC When radius is 3cm, charge enclosed is -10+10 +5? I'm unsure where the 5mC is here in this...

Since it is stated that ##E'_x = E_x##, I am going to set a special case where ##z' = z = 0##, ##E_x## in (5.10) reduces to, ##E_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{x^2}## However, ##E'_x## in (5.13) reduces to, ##E'_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{\gamma^2 x'^2}## There is an...

I have a question relating DAC architectures. The guts of the question are really to do with capacitors and charge. I want to see if my understanding is correct. This is not a homework question or anything, just thinking about how the circuit interacts. Setup: Consider the following setup...

Suppose we have an accelerometer carrying a charge. The charge density everywhere in the instrument is uniform, or at least what I mean to say is, the charge on any component is proportional to that component's mass. Now, in an inertial reference frame, we place the accelerometer in an electric...

I found two formulas to calculate the work done. One is with this path integral: ## W_{AB}## = W(## r_A,r_B ##)=q* ## \int_{r_A}^{r_B} E*dr ## but here is the one I tried to use: ## W_{AB}## = q*Δ U = q*(## \frac {kQ} {r_A} ## - ## \frac {kQ} {r_B} ## ) Now here's my problem, what are...

I have in my notes the charge conjugation operator converts the spinnor into its complex conjugate , ## C\begin{pmatrix} \varepsilon \\ \eta \end{pmatrix}=\begin{pmatrix} \varepsilon^{*}{} \\ \eta ^{*} \end{pmatrix}##when applied to gamma matrix from dirac equation does it do the same...

Based on the conditions, I found that $$V(x)=\frac{a^2}{\pi^2} ρ_0sin(πx/a)$$ would be a solution to Laplace's equation for $$|x|\leq a$$ and $$V(x)=cx+d$$, where c and d are constants. From the boundary conditions, $$\frac{dV(a)}{dx}=\frac{a}{\pi} ρ_0cos(πa/a)=ac$$, $$c=\frac{a\rho}{\pi}$$ and...

This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...

I first tried to use the Gauss' law equation E.A = q/ε0 to find the total charge enclosed. The answer came out to be q(enclosed) = 4πqε0e^(-4r). So for r approaching infinity, q(enclosed) approached 0. Next, I tried the equation ∇·E = ρ/ε0, calculated rho to be -4qε0e^(-4r)/r^2 and total...