Elecrostatics Definition and 104 Threads

Following my instructor's notes the statement of the Uniqueness Theorem(s) are as follows "If ##\rho_{inside}## and ##\phi_{boundary}## (OR ##\frac{d \phi_{boundary}}{dn}## ) are known then ##\phi_{inside}## is uniquely determined" A few paragraphs later the notes state "For the field inside...

1. Two identical flat plate capacitors are inserted in each other. First, none of the plates was charged, but then they have been connected to sources of current, keeping the constant voltage ## V_1 ## and ##V_2 ##. Find the potential difference between inner plates, which are kept at the...

In electrostatics, for what I understand the when I have an electric field, the density of the energy stored in it is given by the following formula: $$W = \frac{1 }{2} E \cdot D$$But when there is some material permantent polarization the above formula fails to work. Is this correct? How can...

Two identical metalic spherical conductor of radii ##R## are at a distance ##d## apart.One of the conductor has charge ##Q## while the another one is neutral.What will be the induced charge on the other conductor ? If we put an image charge ##q## inside the neutral one. Then the potential at...

1. We've been given a spherical capacitor with radius of 1 cm for inside electrode and 2 cm for outside electrode. Voltage between electrodes is 360 V and the task is to find largest and smalles electric field strength in capacitor.2. I'm not sure how voltage given in capacitor works and how to...

I've been thinking about this problem and would like some clarification regarding the value of the divergence at a theoretical point charge. My logic so far: Because the integral over all space(in spherical coordinates) around the point charge is finite(4pi), then the divergence at r=0 must be...

The permittivity of free space, ε0, is usually given without any derivation or historical context as to how it was experimentally determined. Could you explain to me how the value of ε0 was first determined experimentally or provide a resource that gives such a derivation? Thanks!

Homework Statement Consider an infinitely long cylindrical rod with radius a carrying a uniform charge density ##\rho##. The rod is surrounded by a co-axial cylindrical metal-sheet with radius b that is connected to ground. The volume between the sheet and the rod is filled with a dielectric...

Lets say I have a conducting neutral sphere containing a spherical hollow space. The hollow space contains a point charge at its center. This setup will result in a charge equal in magnitude with opposite sign of the point charge spreading evenly over the boundary of the hollow space and a...

I am preparing for an exam which requires me to solve problems in electrodynamics and electrostatics problems along with classical mechanics and geometrical optics problems. The concern is that I do not have electrodynamics in my course in school so I have to study it completely on my own. I...

In basic electrostatics any charged particle will produce an electric field at every point in space, and will have electric filed lines spreading out radially. E = kQ/r^2 The Standard model of particle physics says that the Photon is the force carrier for the Electromagnetic force, just like...

Homework Statement :- electric field vs position how to plot it[/B]Homework Equations :- force per unit charge[/B]The Attempt at a Solution :- i know option 1 and 2 can never be an answer to this question but still i am confused between 3 and 4 option and help me solve with proper equation[/B]

Homework Statement Having a conducting sphere with radius ##R## and charge ##Q##, dielectric is put on it so that a spherical shell with inner radius ##R## and outer radius ##3R## is formed. Calculate: 1. Electric permitivitty ##\epsilon## such that ##E(r), R<r<3R## is constant and there's...

Hi, I have some confusion about the jump conditions for an electric field across an interface between two materials with different properties. In general, we have the two jump conditions across an interface: n.(ɛE)+ - n.(ɛE)- = σ...

Homework Statement A neutral atom with known polarizability α is located at the origin. A point charge Q is situated on the y-axis a large distance d from the atom. (The atom therefore becomes polarized due to the electric field of the point charge.) (a) Find the electric field due to the atom...

I have a non conducting sphere with a charge ρ=A/r per uni vollume A is constant. suppose there is a cavity in the centre and within a particle of charge q. i want to find the E inside the sphere in respect with r. Homework EquationsThe Attempt at a Solution for radius equal of the cavity i get...

There is a big sphere with charges distributed on the surface. N charges are distributed on a patch of the sphere (all the information of the charges such as their locations are known). Suppose the rest of the sphere has similar charge distribution as the patch, how to approximately calculate...

Homework Statement (This is not a HW problem, but HW-type problem.) A half cylinder of radius R and length L>>R is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of...

I was wondering what force hold together like charges in capacitor, battery... we have a capacitor having two oppositely -charged plates so my question is what holds the electrons with electrons in one plate and what holds protons with protons in other plate since like charges repel each other...

Homework Statement Three insulated concentric spherical conductors, whose radii in ascending order of magnitude are ##a, b, c##, have charged ##e_1, e_2, e_3## respectively, find their potentials and show that if the inner most sphere is grounded, the potential of the outermost is diminished...

Homework Statement Two charges 2q and -q are located at x = 0 and x = a respectively. There are field lines extending from the positive charge and lines going inwards to the negative charge. Some of these lines go from the positive charge to the negative, but some go off to infinity from the...

Homework Statement :[/B] This is isn't exactly a problem,but actually something i don't understand in the book i was following, so there this art. about 'Principle of a Generator', whose description is given as, " A generator is an instrument for producing high voltages in the MeV range. Its...

I need to draw electric field lines of sphere in uniform electric field with LaTeX/TikZ. Can anyone show me equation of field lines in polar coordinates?

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...

Here is the experience: I put two electrodes inside paraffin oil (separated by at least 3cm), and submitted the electrodes to high voltage. At 20000 V - 30000 V, strong streams can be observed inside the paraffin oil. Since paraffin oil is a good dielectric, I just would like to understand the...

Homework Statement Homework Equations \overrightarrow{F} = \frac{1}{4\pi\epsilon_0}\frac{qQ}{r^2}\hat{r} The Attempt at a Solution I found to hard summarizing all forces directly adding each to other. The solution of this problem is only matter of drawing the 13-sided polygon and forces...

This is a question born out of a homework thread that lead to a discussion between @haruspex, @rude man, and myself. Link here https://www.physicsforums.com/threads/what-is-the-charge-of-each-conductor-afterwards.923909/ . I feel this question deserves its own thread and hopefully we can get...

Homework Statement I have 2 thin rods of length L in the axial plane(x axis), they're of the same uniform linear charge distribution and are separated by a distance a . Homework Equations $$E = \frac{kq} {R^2}$$ $$F = qE$$ The Attempt at a Solution [/B] Let 0 be one at one end of the two rod...

I am having hard time understanding the definition of work done to move a charge in an electrostatic field book says that if charge A and B sitting at some position and now if I move the charge say A towards B from arbitrary direction that force required is exactly equal and opposite to the the...

I am designing a device, which will utilize an electric field. The question I have run into is whether or not the current is treated as the charge enclosed for Gauss' Law, or if there's another way I would calculate it. Also, am I correct that the voltage of the circuit would be different than...

Homework Statement A uniform electric field exists in the region between two oppositely charged parallel plates 1.59 cmapart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.50×10−6 s . Find the...

Homework Statement I am trying to derive the dipole-dipole interaction derivation, which is: U=(-p1p2/4πϵ_0) (1/z^3) ((2cosθ_1cosθ_2)− (sinθ_1sinθ_2cosζ)) Where p1 and p21 are the two dipole moments, r is the distance between two dipoles on the y axis, θ_1 and θ_2 are the angles between the...

potential energy is the work done by an external force in taking a body from a point to another against a force. on the surface of a conductor the electrostatic charges arrange themselves in such a way that the net electric field is always zero. so if there isn't any force to act against why...

Say, we have two particles of equal and opposite charge in an isolated system in which we neglect gravity. The energy of particle 1 is: E1 = U1 + T1 Where U1 is electrostatic potential energy and T1 is the kinetic energy of particle 1. The energy of particle 2 is: E2 = U2 + T2 Where U2 is...

Homework Statement I am trying to calculate the theoretical time that it takes for a small piece of aluminium foil on a bottom plate to reach a top plate. The plates have a potential difference created by a 3kV Cockcroft–Walton generator. The plates are short cylinders with a surface area of...

I have a function of the cartesian coordinates x, y, z such that: f = a * ln|sin(px + iqy)| + by + c This equation should be describing the electric field nearby the wall of the Faraday cage. I solved the Laplace equation Δf = 0 and got : p = +/- q, so p = q. I should choose the constants...

Homework Statement There is a total of ##Q## charge on soap bubble of radius ##R##. What force is acting on one hemisphere by the other ? Homework Equations Electrostatic pressure is ##P_e = 2\pi \sigma^2## for a spherical shell. The Attempt at a Solution ##P_e = F/A## therefore ##F =...

Homework Statement Two charges placed at circumference of a circle of radius ##a## at ##\pi/2## from each other. Find the relative magnitude of third charge kept on the circumference such that the system is at equilibrium.Homework Equations Coulombs law. The Attempt at a Solution Let ##Q##...

refer only to the image above, not the question 4.) Two point charges, Q1 and Q2, are placed 0.30 m apart on the x–axis (shown in the figure above) Charge Q1 has a value of –2.50 x 10–6C. The net electric field at point P is zero. a. What is the sign of charge Q2? ____ Positive ____...

I need help trying to set up this problem. I want to find the capacitance between a point charge and a finite plate (or disk) as the point moves from above the center of the plate to some distance off the plate. I have been able to simulate this problem using FEM, however, there should be a...

I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is...

Homework Statement At our university we were given this problem: charged ball with mass of ##m = 0.0001 kg## and charge ##Q = -10^{-5} C## is placed on geometric axis of thin torus with inner radius of ##r_{inner} = 0.05 m##, outer radius of ##r_{outer} = 0.1 m## and surface charge density...

Homework Statement An infinite line charge (wire) has lambda = lambda0. It produces an electric field of magnitude 5E4 N/C at a distance of 2m. Determine the typical force between two adjacent extra electrons in the wireHomework Equations E_line = lambda/(2pi*r*epsilon0) The Attempt at a...

Homework Statement Two hollow metal spheres (left one has radius of 0.7 meters and right one has radius of 0.4 meters) are half-submerged in the sea water with specific conductance of γ = 4 S/m. Distance between their centers is much greater than their radii dimensions and equals 60 meters...

Hey everyone Just a picture of my configuration. The assumption here is $$\epsilon_a,\epsilon_b,\epsilon_c$$ are different from one another. Really the interest of this problem is to find the scalar potential $$\phi$$, such that $$\nabla^2 \phi = 0$$. So now my question, about jump...

Homework Statement A slab of dielectric of thickness a and relative permittivity ε is placed in a uniform external field E whose field lines make angle θ with normals to the surface of the slab. What is the density of polarization charge on the surface of the slab? Neglect end effects...

I have spent hours on the web and in libraries to obtain a general and careful approach to the notion of capacitance, without success. Please, read carefully the question: I already know the usual blabla about capacitance. Also, I appologize in advance for the length of this question. I...

This may well be a textbook question, or even a duplicate in this forum, but I have no idea of how to compute the capacitance between two conductors in the general case: all the computations I saw in textbooks make heavy use of symmetries to compute the capacitance, e.g. capacitance between two...

Homework Statement A dielectric sphere of radius R with uniform dielectric constant ε has an azimuthally symmetric density charge σ = σ0 cos θ placed on the surface. Outside the sphere is vacuum. (a) Obtain the electrostatic potential inside the sphere, φin. (b) Obtain the electrostatic...

I know there is a lot of answers out there, but so far none really answered my question. Say I have this radioactive conductor sphere that has a negative charge. Of course, all the negative charges will be spread evenly on the surface and there SHOULD be 0 electric field inside the conductor...