Electrostatic potential Definition and 138 Threads

Homework Statement I am working on a problem that states the following: Imagine an infinite straight wire carrying a current I and uniformly charged to a negative electrostatic potential Φ I know here that the current I will set up a magnetic field around the wire that abides to the right...

Homework Statement "An object is moving in a straight line from a positively charged area (A) to a negatively charged area (B). Explain how the electrical force and electrostatic potential energy experienced by the object will vary when it is neutral (has no charge)." Homework Equations N/A as...

Homework Statement What is the electrostatic potential for the electric field in the region x ≥ 0 where: E = (E0)*e^(kxi) V/m, with E0 a constant? (The potential at x → infinity is defined to be zero). Homework Equations b v = v_a - v_b = - ∫ E . dl...

Homework Statement E=(1/4πε0)(Q/r^2) for R<r<2R Homework Equations U= integral (2R,R) ( (ε0 E^2)/2*4πr^2 dr The Attempt at a Solution I have no idea where the U-formula comes from. Any help would be appreciated. I added some pictures so that it could be easier to understand.

Homework Statement Determine the total electrostatic potential energy of a nonconducting sphere of radius r_0 carrying a total charge Q distributed uniformly thorughout its volume. Homework Equations U = qV The Attempt at a Solution \rho = \frac{Q}{4/3\pi r_0^3} = \frac{dq}{4\pi r^2dr}...

Homework Statement Assume that the electrostatic potential of a point charge ##Q## is $$ \Phi(r) = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^{1+\delta}},$$ such that ##\delta \ll 1##. (a) Determine ##\Phi(r)## at any point inside and outside a spherical shell of radius ##R## with a uniform surface...

Homework Statement Find the Electrostatic potential energy of a cubical configuration of point charges as shown in the figure. Each of the charges is 5.00e and the edge of the cube is 2 cm. (The image is simply a cube with one of the points labeled q) Homework Equations U=kQq/r The Attempt at...

Homework Statement Question Homework Equations Equation The Attempt at a Solution Attempt I am not sure how to write the |r-r'| in a way that allows me to actually solve the integral. I have tried writing |r-r'| in spherical co ords, but all I seem to be able to get is this as the separation...

Homework Statement A spherical conducting shell of radius R is held at a potential V0. Outside the shell, the charge density is ρ(r) = ρ0sinθcosφ for R < r < 2R. Find the electrostatic potential everywhere outside the shell. Homework Equations Green's function in spherical coordinates between...

Homework Statement I need to find the green function for a dielectric sphere (\epsilon_1) inside another dielectric medium (\epsilon_2) using the method of images. Homework Equations In gaussian units I have: \phi=\frac{q}{\epsilon|r-r1|} The Attempt at a Solution Due to the symmetry of the...

Homework Statement Find the energy stored in a solid sphere by integrating ##\frac{\epsilon_0}{2} \int E^2d^3r## given that ##E=k\frac{r^2}{4 \epsilon_0}## for ##0<r\le R## and ##E=k\frac{R^4}{4r^2 \epsilon_0}## for ##r>R## Homework Equations ##U=\frac{\epsilon_0}{2} \int E^2d^3r##The Attempt...

When determining potential energy we have the relationship: PE = V*q = E*q*d But depending on the scenario we can't use them interchangeable right? If you want to calculate the work needed to be done by a particle going from a distance Y to right next to another particle of the same charge...

Homework Statement A box shaped rectangular metal cavity of sides a, b and c along the x, y and z axes, respectively, has one corner at the origin. Of the six sides, all are grounded except the one at x=a and the one at y=b which are held at potentials of V1 and V2 , respectively. Find the...

In a vacuum under standard gravity, an anchored spherical metal electrode is brought to +1,000,000 volts relative to the distant walls of a much larger chamber. (I'm a new user; hopefully this will display as attachment 1) Therefore, electrons that fall through a small gap in the electrode...

I'm a little stumped with this problem, I have posted a photograph below as there is a diagram to compliment the questionExpressions which I used where V(r)= k q/r Where q= σ da Where da is an element of area And k= 1/4πεI messed around with these expressions for a while but it didn't really...

Hello everyone I am stuck with a problem about voltages (electrostatic potential) and forces. According to capacitor equations the energy stored in the capacitor is: U=1/2*C*V^2 And force is: F = - dU/dx Since U is dependent on V^2, our force can’t be positive (repelling...

What is the criteria in choosing infinity as zero potential ? e.g. an infinite plate with uniform charge density. What is the physical meaning of not be able to choose a position as reference potential ??

Problem #1 A slab of thickness 2a (extending infinitely in the y and z directions) with non-uniform charge density is parallel to the yz-plane. The charge density is given by ρ(x) = γx2, -a < x < a where γ is a constant. 0, a < |x|. (a) Use Gauss's law plus symmetry to find...

Homework Statement Consider a series of three charges arranged in a line along the z-axis, charges +Q at z = D and charge -2Q at z = 0. (a) Find the electrostatic potential at a point P in the x, y-plane at a distance r from the center of the quadrupole. (b) Assume r >> D. Find the...

1. The problem is in the attachments. 2. Field strength is equal to voltage divided by distance 3. I want to make sure that i understand a few things before i solve this problem! i would like to know your opinion! a) first, field strength is inversely proportional to the the distance squared...

Homework Statement A space probe travels towards a planet measuring the electrostaticpotential as it approches. the electric field strength is -500 N/C at the altitude of 600,000 KM and it decreases steadily until it reaches -400 N/C at 580,000 KM above the planet's surface . find the...

How do I know if E (electric field) and \Phi (electrostatic potential) is continuous at the surface? I'm asking this because I have a problem choosing which formula to use, if you know what I mean. There are a lot of formulas for E and \Phi .

Homework Statement A conducting sphere of radius ##a## carries an initial charge ##q_o##. It is surrounded by another concentric sphere of radius ##b##. The space between the two spheres is filled with a dielectric of permittivity ##\epsilon## and conductivity ##\sigma##. Find the electrostatic...

Homework Statement I'm currently tackling parts (a) and (b) of section ii) decribed here:http://puu.sh/31KIZ.png Homework Equations V=(q/4∏ε)*(1/r) The Attempt at a Solution From the first section (i) calculating the potential was relatively straight forward since we were only...

Working from Krane's Modern Physics 11.5 Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice. I believe the formula I'm supposed to use is U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R} Just from looking in the chapter I can...

Hello, (this isn't homework but I thought it wasn't worthy of the main forums) I'm looking to clarify some thoughts about the various forms of electrostatic potential energy. As I understand, the expression \displaystyle \frac{\epsilon_{o}}{2} \int \textbf{E} \cdot \textbf{E} \; dV over all...

A conducting spherical shell of radius 11.0 cm is charged to a potential of 5.00*10^4 V. What is the value of the electrostatic potential 5.0 cm outside the surface of the sphere? V=(1/[4*pi*(epsilon naught)])*(Q/r) <-- outside of the shell V=(1/[4*pi*(epsilon naught)])*(3Q/2R) <-- inside...

Homework Statement The diagram shows two charges, +4 μC and –16 μC, 120 mm apart. What is the distance from the +4 μC charge to the point between the two charges where the resultant electric potential is zero? A 24mm B 40mm C 80mm D 96mm Homework Equations potential equation...

Homework Statement Determine the total electrostatic potential energy of a nonconducting sphere of radius r0 carrying a total charge Q distributed uniformly throughout its volume. Express your answer in terms of the variables Q, r0, and appropriate constants. Homework Equations V = kQ/r...

i'm trying to understand how the electrosatic potential expressed as an integral satisfies poisson's equation. i know that i have to take the laplacian of both sides of (Eq 1.17) page 35 in Jackson. i understood how jackson took the laplacian of \frac{1}{\sqrt{r^2 + a^2}} but after Eq 1.30...

Homework Statement There is a charge q, at a distance d from an infinite conducting plane (z=0). Determine the electrostatic potential drop between the z=0 and z=d. Homework Equations Ohm's Law DeltaV=-integral (E.dl) The Attempt at a Solution I know how to do this problem...

If I have a sphere with radius R which has a charge distribution given by \rho(r)=\frac{5Q}{\pi R^{5}}r(r-R) and \rho = 0 at r bigger or equal to R, how do I find the electrostatic potential of this overall space? There is a charge Q, in addition, at the origin. My original thought...

Homework Statement Use Green's Reciprocation Theorem to show the G.S to the Electrostatic PotentialHomework Equations Green's Reciprocation Theorem \int_{v} \rho^{'} \Phi d^{3}x + \int_{s} \sigma^{'} \Phi da = \int_{v} \rho \Phi^{'} d^{3}x + \int_{s} \sigma \Phi^{'} da The...

Hi all, I am considering the situation illustrated in the schematic below. A surface density of permanent charges σ is embedded into a dielectric (with relative permittivity εr) itself sandwiched between two electrically floating metallic plate. We have also L>>t1 and L>>t2. My first goal is...

Homework Statement The electrostatic potential at each point in the region 4x^2 + 9y^2 <= 36 is given by f(x,y) = 3x^2 + 2xy - y^2 + 5. Find the maximum potentials in the region. (Without using Lagrange Multipliers). The solution also said how to do it with Lagrange Multipliers but I...

Homework Statement Homework Equations PE = -Fdcos(theta) PE = -(qE)dcos(theta) PE= -pdcos(theta) or PE = - pd since all the angles here are nice. where p is dipole The Attempt at a Solution :( beyond trying to find what looks like the answer, I'm not sure many thanks!

The Dirac electron in the Higgs vacuum field v and an electromagnetic field with vector potential A_\mu is described by the following equation: i \gamma^\mu \partial_\mu \psi = g v \psi + e \gamma_\mu A^\mu \psi where g is the coupling constant to the Higgs field and e is the coupling...

Homework Statement At the surface of a conductor the potential is constant .. I can't get my head around this .. Homework Equations E=-grad VThe Attempt at a Solution The only reason I can think about this is Electric field is perpendicular at the surface , hence no work is done when moving...

Homework Statement The charge distribution of an atomic nucleus is modeled by the Gaussian distribution: p(r) = A exp(-r2/a2) Obtain the Fourier transform of p(r), and use the result to obtin an expression for the potential as a Fourier integral. Homework Equations Fourier transform and...

There is one point I am unclear upon in terms of indued charges. If a charge is induced by another charge, will the potential from the induced charge have an effect on the inducing charge. It seems that if it were the case you would be getting (increasing) energy from nothing, however if it...

My textbook says that Electrostatic potential is the work done on a unit charge to bring it from infinity to a point from a given charge without acceleration, against the electric field presend due to the given charge. So, as it says that there will be no acceleration, does it imply that...

Homework Statement Two identical conducting spheres, with a radius of 15.0 cm, are separated by a distance of 10 m. What is the charge in each sphere, if the potential of one sphere is +1500 V, and the potential of the other one is -1500 V? Which assumptions did you make? Homework Equations...

Homework Statement Given a charged metallic spherical shell of radius a=2.75cm, with a potential of 2.5kV a distance of r=6.0cm from the center of the shell, what is the charge on the shell? Calculate the potential on the surface of the shell.Homework Equations V=kQ/rThe Attempt at a Solution...

Homework Statement C120 uF C2=40uF C3= 50uF if no capacitor has the capacity to bear more than 50V then maximum potential difference between the two ends is Homework Equations Q=CV The Attempt at a Solution i tried by calculating the Ceq then putting it in the equation finding...

Homework Statement The figure shows a section of a cylindrical surface, height h and radius R. The curved surface extends from the z-axis to the y-axis only and has a charge density given by σ(z)= σ0z where σ0is some constant. ind the electrostatic potental at a. (a is at the origin) I'm...

Homework Statement Two large flat parallel sheets have opposite uniform surfacecharge densities ±σ and are separated by a distance d. Alarge uncharged conducting slab of thickness d/3 is parallel thethe charged sheets, centered between them. Find the electrostaticpotential as a function of...

Homework Statement Two dust particles are separated by 0.01m and of the same mass and charge, find the total potential energyHomework Equations E_{el}=k\frac{q_1 q_2}{r} E_{grav}=-G\frac{m_1 m_2}{r} r=0.01 m, q_1=q_2=1.1201\times10^{-18} C m_1=m_2=13\times10^{-9} kg Where G and k are the...

Hi, I am trying to do the multipole expansion of a point charge away from the origin, I can't understand Legendre polynomials so want to do it in Cartesian but when I try to Taylor expand the \left|\frac{1}{\vec{r}-\vec{r'}}\right| I am not sure how to handle the modulus. Any help...

Everyone knows that the potential difference between two points 1 and 2 is given by \int_{1}^{2}{\vec{E}}\cdot d\vec{l}. My question is that can we calculate the potential difference between two point charges by this formula? Say, one of them is +ve charge and the other is a -ve charge...

Thinking in terms of electric circuits and electrostatic potential I understand how an electric current arises as manifestation of a difference in potential. How does this work at a more microscopic level? I.e. how does an electron know what potential it's environment is at? E.g.: If I...