Electrostatic energy Definition and 39 Threads

I keep reading the amusing lectures from Feynman on Electrodynamics. In particular in Lecture 5-8 figure 5-10, he argues that touching a charged hollow sphere externally with a litte metal ball will cause the ball to pick up charge from the charged sphere (contrary touching the hollow sphere...

I think it is negative because of the ##g_{\mu \nu}## metric tensor, but I am not sure.

As a preliminary note, most people flex about how dumb questions and then continue to school and scold curious minds. Instead of taking a demeaning approach I just ask for respectful insight to quench curiosity. I will 1) explain the experiment as I know it to be, 2) explain what I have been...

Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...

Electrostatic energy involves a volume integral and a surface integral The question is how to apply this formula to a finite space in which case the 1st term (surface integral) won't vanish. Let's apply to a capacitor and enclose the capacitor by a closed surface. Calculate the energy integral...

I know the energy is ##\frac{q²}{ 8 \pi \epsilon_{0}}( \frac{1}{a} - \frac{1}{b})##, but I can't get this result using the second equation. What I did: ##W = \frac{1}{2} \int \rho V d \tau ## ##\rho = \frac{q}{ \frac{4}{3} \pi r³}, a < r < b ## ##V = \frac{q}{4 \pi \epsilon_{0} r}## ## W =...

I tried to use ##W = ε_0/2 \int E^2d\tau## for all space. So I find that ##E = \frac{(R^3 - b^3)\rho}{3ε_0r^2}## where ##\rho## is the charge denisty. So from here when I plug the equation I get something like $$W = \frac{(R^3 - b^3)^2\rho^2 4 \ pi}{18ε_0} \int_{?}^{\inf}1/r^2dr$$ Is this...

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...

Please refer to the image attached. So, my doubt is: While calculating dW in the derivation, we know this work is being done by external force, because only then the unit positive charge can be made to move towards the charge +Q. So dW should be equal to Fext.dx but here in the book it is shown...

Homework Statement fig 1 : Area of each plate is S, separated by 2d, charge Q in the capacitors fig 2 : uncharged conductors of area S, thickness d, inserted parallel between plates What is the ratio of electrostatic energy in fig 2 to electrostatic energy in fig 1? Homework Equations Q =...

A charge of +2.5 micro coulomb is at the origin and a +3.5 micro coulomb is at the point (3,0). What is the velocity of a proton when it is at (6,0) if it was released at (5,0). My solution: $$E_0=E_f$$ $$PE=KE$$ $$Since...Work = -PE$$ I can calculate the work it takes to move the proton from...

Homework Statement Two equal charges of magnitude Q each are placed at a distance d apart .Their electrostatic energy is E. A third charge -Q/2 is brought midway between these two charges .The electrostatic energy of the system is now A) -2E B) -E C) 0 D) E Homework Equations EPE = kq1q2/r...

Homework Statement We have a spehere of radius ##r_1## and on of ##r_2## far away from each other. The first sphere has a charge ##Q##. What is the change in electro static energy when they are connected together? Homework Equations Potential of a charged sphere: ## V = \frac{Q}{4\pi\epsilon_0...

Homework Statement We model the Hydrogen atom as a charge distribution in which the proton (a point charge) is surrounded by negative charge with the volume density of ρ = -ρ0 * exp (-2r/a0) where a0 is the Bohr radius. And ρ0 is a constant chosen such that the entire atomic distribution is...

I am learning in Electrostatics that the work done to construct a charge configuration is ∑qV and when we assume that charge is not discrete but continuous we get the work done to be ∫E.Edv and hence we say that the energy stored in electrostatic field is ∫E.Edv. when applying this formula to...

Suppose there are N charges fixed at arbitrary locations , how do I calculate the total electrostatic energy ? I can think of two ways. one being the straightforward coulomb's law : k=1/(4*pi*ε) Q=k/2 * ΣiΣj qiqj / |ri-rj| ; i≠j the other method is to integrate energy density with respect...

Homework Statement A spherical conductor of radius ##a## carries a charge ##q## and also there is a jelly of constant charge density ##\rho## per unit volume extending from radius a out to radius ##b##. Find the electrostatic energy stored in the configuration. Homework Equations ##\oint...

Question: "Given an electrostatic potential energy of -6.16x10^-18 J and a distance of 1.12x10^-10m, what is the nuclear charge if there is a single electron interacting with the nucleus?" Okay, Equation: PE = [K*Q1*Q2]/d Where K is a constant of 8.99*10^9 J*m/c d is giving at 1.12*10^-10m PE...

Homework Statement There are 2 small metal balls of radius r1 and r2 and are kept at very large distance , what should be ratio of charges on them for electrostatic energy to be minimum Homework Equations E=Q^2/(8πϵR) Self Energy The Attempt at a Solution In this problem, electric...

I'm trying to think about what it is I should be considering before I start throwing up some maths. I'm thinking to assume that the positively charged core is a point charge +e and the electron is uniformly distributed over a sphere of radius Rs. The self energy of the electron...

Homework Statement Homework Equations work = kqqq/(distance) The Attempt at a Solution http://i33.photobucket.com/albums/d86/warnexus/electrodiag.jpg

Homework Statement Determine the electrostatic energy, W, of a spherical shell of radius R with total charge q, uniformly distributed. Compute it with the following methods: a) Calculate the potential V in spherical shell and calculate the energy with the equation: W = (1/2) * ∫σVda...

Homework Statement Compare the electrostatic energy of two opposite charges e and -e, a distance 7 angstroms apart in water at room temperature and that in vacuum (express the energy in terms of Bjerrum length) Homework Equations E = 1/(4(p\pi\epsilonD)*(-e^2)/r^2 ? The Attempt at a...

A solid sphere carries a uniform, surface-charge density. The sphere is surrounded by a linear dielectric with electric susceptibility, κ. For which system is the electrostatic energy the largest. a) For the sphere alone. b) For the sphere and the dielectric. c) Both systems have same...

Battery has positive and negative charges, will it be possible to generate electrostatic energy to my body by touching either sides of battery? Thanks in advance for any suggestions

When I play with my cat, there is some electrostatic energy generating between my hands and cat's fur, does anyone have any suggestions whether my body get positive charges after playing with my cat or negative charges? Thanks in advance for any suggestions

Homework Statement For two concentric conducting spheres (radius a and b, b>a) that form a capacitor with charge q on the inner sphere and -q on the outer sphere, express the electrostatic energy in terms of q and -q and the potential difference between them.Homework Equations Gauss's Law, the...

This is actually a question pertaining to a paper I'm trying to understand (PRB 73, 115407 (2006)), but I decided to put it here just to be safe. Homework Statement The paper I'm reading involves starting with an electrostatic energy contribution, and rewriting it with a green's function...

Homework Statement if the separation between the plates of an isolated charged parallel-capactior is increased, why does the stored electrostatic energy increase? Homework Equations C=eA/d e= permitivity of space The Attempt at a Solution i do not know the equation of...

When an electron and a positron annihilate, they typically produce two gamma rays, each of energy mc^2 plus whatever kinetic energy available before annihilation. I was recently told that it is an experimental fact that the electrostatic energy between the electron and the positron does NOT...

http://farside.ph.utexas.edu/teaching/em/lectures/node56.html By equation 595, electric energy in the universe caused by an electric field is derived as http://farside.ph.utexas.edu/teaching/em/lectures/img1261.png. However, how come you can differentiate with respect to volume and say that...

QUESTION: Calculate the electrostatic energy of a homogeneously charged sphere of Volume V and compare the result with 2 times the electrostatic energy of a homogeneously charged sphere of V/2. SOLUTION: OK, so we have a charge Q which is uniformly distributed within a sphere of...

1. Find the electrostatic energy of a neoprene sphere or ratio R, charged with Q if: a) Q is uniformly distributed in surface The Attempt at a Solution So, I can calculate the displacement field (so that I can use the expresion U= \int \vec{D}.\vec{E} dV), but only for those points in...

The original web http://farside.ph.utexas.edu/teaching/em/lectures/node56.html Reading the web which is posted above I got a question ... I need some masters to help me! My question : why not to remain the left term of eq539 instead of eliminating it by "Let us...

hey, i have a question from an exam paper which isn't worded too nicely (most of the questions on the exam are worded in similar ways ) The way I've done it is to first put in my first shell of infintesimal charge and then treat it as a point charge. Then i treat the next shell as just a point...

Homework Statement A solid sphere contains a uniform volume charge density (charge Q, radius R). (a) Use Gauss’s law to find the electric field inside the sphere. (b) Integrate E^2 over spherical shells over the volumes inside and outside the sphere. (c) What fraction of the total electrostatic...

Homework Statement A charge Q is at the origin. A second charge, Qx = 2Q, is brought to the point x = a and y = 0. A third charge Qy is brought to the point x = 0, y = a. If it takes twice as much work to bring in Qy as it did Qx, what is Qy in terms of Q? Homework Equations My main problem...

i don't quite understand the derivation of mutual electrostatic energy of two charged system: U_12=\frac{1}{4\pi}\intE_1(dot)E_2dV=-\frac{1}{4\pi}\intE_1(dot)\nebla\phi_2 dV= \frac{1}{4\pi}\int \phi_2(dot)\nebla(dot)E_1=\int \phi_2*\rho_1dV i undersantd that we are using here...

Griffiths : Electrostatic Energy I'm having a little difficulty in understanding how one arrives at the following expression for electrostatic energy of a continuous charge distribution. W = \frac{\epsilon_o}{2}\int (\vec{E})^2d\tau This result is obtained when the volume of integration...