Electrostatic Definition and 136 Discussions

Electrostatics is a branch of physics that studies electric charges at rest.
Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was thus the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law.
Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.

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  1. C

    I Where to find this uniqueness theorem of electrostatics?

    There is a nice uniqueness theorem of electrostatics, which I have found only after googling hours, and deep inside some academic site, in the lecture notes of Dr Vadim Kaplunovsky: Notice that the important thing here is that only the NET charges on the conductors are specified, not their...
  2. S

    The meaning of the electric field variables in the boundary condition equations

    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...
  3. E

    Boundary conditions (E and D) for a dielectric sphere

    Since there is no free charge ##\int_S \vec{D} \cdot d\vec{a} = 0## and ##\rho_f = 0## ##\sigma_f = 0## ##\vec{nabla} \cdot \vec{P} = 0## since P is a constant ##\rho_b = - \vec{nabla} \cdot \vec{P} = 0## For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss'...
  4. samy4408

    I Weird question in electrostatics -- Work done bringing two positive charges together

    in a cours of electrostatic when we have a positive charge and we bring another one (also postitive)we have to do work and apply a force that equals the force of repultion over the distance which seems wierd because if we do that the net force will be equal to 0 and the charge will not move can...
  5. Hamiltonian

    Find the charge density on the surface of a dielectric enclosing a charged sphere

    The net Electric field(inside the dielectric): $$E_{net} = \frac{1}{4\pi \varepsilon_0 \varepsilon_r} \frac{q}{r^2}$$ $$\vec E_{net} = \vec E_{applied} - \vec p$$ where p is the polarization vector. let charge ##q_{-}## be present on the inner surface of dielectric and ##q_{+}## on the outer...
  6. V

    Force acting on a charge across a hybrid medium

    The force on charge ##q_2## will depend on the electric field in medium with dielectric ##K_2##. Electric field in this second dielectric due to ##q_1## is ##E = \dfrac {kq_1} {K_2r^2}## where r would be the distance from ##q_1##. So, the electric field at the point where charge ##q_2## is...
  7. mohammed

    Where I can find similar examples to this kind of question? "given the electric field. E = (-3 / x*e0)i, find the charge density."

    I'm preparing for exam but it seems I can't find problems similar to this on the internet. Here I will apply Gauss's law on the electric field vector to get the charge density. but the problem is that I can't find similar examples on the internet that uses direct vectors on Maxwell's equations...
  8. V

    Dipole placed in a uniform electric field

    My understanding is that the uniform electric field ##\vec E## cannot be the net electric field since the dipole creates its own electric field as shown in first diagram below, which must superimpose with the uniform electric field. So, yes, the uniform electric field ##\vec E## around the...
  9. nazmulhasanshipon

    Comparing energy lost by the battery & energy gained by the capacitor.

    Imagine the two terminal of a *parallel-plate capacitor* are connected to the two terminal of a battery with electric potential difference #V#. If the capacitance of the capacitor is #C#, and the area of each plate is $A$. In this process would the energy lost by the battery and the stored...
  10. V

    Reason for glass rod losing electrons

    I am not sure if the explanation below is enough. This is a high school level question. When rubbing occurs between glass and silk, then heat energy is produced which provides the energy needed to free up electrons in outermost orbits of atoms in silk or glass. But silk has very tightly bound...
  11. jackiepollock

    How to picture a radial field around a 3d object?

    Hello! First off, for a), I am not too sure how to picture a radial field around a 3d object. I know that this spherical metal dome is basically a enlarged version of an atom, but since with problems on radial field around an atom, I don't have to consider its diameter, I'm not sure how the...
  12. jackiepollock

    B Problems regarding electrostatic forces in everyday levitation

    Hello! I'm reading this part of the A-level physics book and finding a few places that I couldn't wrap my head around. They are underlined. 1) When saying oxygen, is it saying that oxygen is the most abundant element in the shoe atoms? 2)I am not too sure why the force per atom is shared...
  13. F

    Kinetic and potential energy of a particle attracted by charged sphere

    Hello, I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...
  14. A

    Capacitance of a parallel-plate Capacitor with non uniform dielectric

    Hey guys! I'm having trouble with the solution that I arrived at. Through boundary conditions I'm able to determine ##\vec{D}## as $$\vec{D}=-\frac{4Q}{R_0^2}\hat{e_z}$$ (In CGS units) Trough that I'm able to get the electric field as $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
  15. V

    A simple question in Electrostatics -- The separation of two balls in an Electric Field

    I used the concept of electrostatic induction, which would cause the charges in metal ball near the ebonite rod to have +ve charges on end next to rod and a -ve charge on the end touching the other ball. What confuses me is how charges separate on the second ball. The only way these balls can...
  16. B

    I How to ensure an equation is dimensionless when it includes "Debye"

    I am trying to check if an expression is dimensionless. If it is, then I have done things correctly. However, I am stuck on how to deal with a (Debye^2) term. How can I break it down to find out if it cancels out with the other units I have left? I know this is probably a trivial question...
  17. P

    Meaning of F = -dU/dx for capacitors

    I have noticed that F = -dU/dx in gravitation gives the attractive force experienced by both bodies. For capacitors, does F = -dU/dx give the force experienced by each capacitor?
  18. D

    A Solution of Poisson's Equation

    We all know that Poissson's equation in electrostatic is: $$\nabla^2\phi=-\frac{\rho}{\epsilon_0}$$ My question is: why the solution, lets say for 1D, is not just double integral as follows: $$\phi=\iint -\frac{\rho}{\epsilon_0} d^2x$$ which gives x square relation. But the actual solution...
  19. Celso

    Superposition in separation method of variables

    Each different boundary condition means a different charge configuration, how can this problem be solved using superposition?
  20. A

    Who invented electric potential and why?

    Why was that concept necessary ?, I know there's also a gravitational equivalent of this concept I couldn't find anything on google Thanks Daniel
  21. qwereqe

    Detect if the Electric Field in a parallel plate capacitor is pointing up or down

    Assuming we have an infinite plane capacitor,where the upper plate is charged positively and the bottom layer is charged negatively. Now we know the field outside the capacitor is zero so we can't tell if the positive charge is on the upper plate or the lower plate. But, if we place it inside...
  22. A

    Potential energy of a system of two punctual charges along the X axis

    I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...
  23. O

    I Is my derivation correct?

    My work is in the following pdf file:
  24. S

    Flux due to a charge located at the corner of a cube

    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...
  25. R

    A doubt on Electrostatics -- An electrified rod attracting light objects

    "When electrified rods are brought near light objects, a similar effect takes place. The rods induce opposite charges on the near surfaces of the objects and similar charges move to the farther side of the object." -from a high school physics book. NCERT Class 12th part 1 to be precise. can...
  26. G

    Gauss-Theorem on a solid dielectric sphere

    The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from...
  27. Elder1994

    Find the electric dipole moment for a water molecule

    The equation that we saw in class is for a continuous charge distribution, I think that for this exercise I need to treat the system as a discrete charge distribution but I'm not sure. Also, I don't know how I can calculate the intensity of the electric field needed to move this charge.
  28. Prabs3257

    Electrostatic force equilibrium

    I was thinking that we can equate the electrostatic potential energy and the spring energy (as the force is similar to that of a spring so energy will also be 1/2kx^2 ) but i am not getting the correct ans but by equating the net force on one charge to kr i am getting the correct ans can...
  29. Boltzman Oscillation

    Engineering How do I find the electric fields for this capacitor?

    the image is given here along with some numerical information: Now I know that the formula for the electric field in a capacitor is given as: $$E = \frac{V}{d}$$ which I can use to obtain the three following fomulas: $$E_1 = \frac{V_1}{d}$$ $$E_2 = \frac{V_2}{d}$$ $$E_3 =...
  30. D

    Find the electric field inside and outside of a spherical shell superposition

    Hi! I need help with this problem. I tried to solve it by saying that it would be the same as the field of a the spherical shell alone plus the field of a point charge -q at A or B. For the field of the spherical shell I got ##E_1=\frac{q}{a\pi\epsilon_0 R^2}=\frac{\sigma}{\epsilon_0}## and for...
  31. D

    What happens when one of two cocentric spherical shells is grounded?

    Hi! I need help with this problem. When the outer shell is grouded, its potential goes to zero, ##V_2=0## and so does it charge, right? ##-Q=0##. So the field would be the one produced by the inner shell ##E=\frac{Q}{4\pi\epsilon_0 R_1^2}##. When the inner shell is grounded, I think that...
  32. peguerosdc

    Understanding Green's second identity and the reciprocity theorem

    This is Jackson's 3rd edition 1.12 problem. So, for both ## \phi ## and ## \phi' ##, I started from Green's second identity: ## \int_V ( \phi \nabla^2 \phi' - \phi' \nabla^2 \phi )dV = \int_S ( \phi \frac {\partial \phi'} {\partial n} - \phi' \frac {\partial \phi} {\partial n} ) dS ## And...
  33. Beelzedad

    I Is my interpretation of this three dimensional improper integral correct?

    In Physics/Electrostatics textbook, I am in a situation where we have to find the electric field at a point inside the volume charge distribution. In Cartesian coordinates, we can't do it the usual way because of the integrand singularity. So we use the three dimensional improper integral...
  34. sergiokapone

    Potentials (and ##\Delta\phi##) of nearby converging bodies

    Let ##Q## - charge of one of conductor, ##\phi_1## --- potential of charged conductor, ##\phi_2## --- potential of uncharged conductor. For the charged conductor: \begin{equation} \phi_1 = D_{11}Q , \end{equation} for uncharged conductor: \begin{equation} \phi_2 = D_{21}Q \end{equation}
  35. M

    What will the electric field be at the surface?

    The electric field due to a dipole distribution in volume ##V'## can be viewed as electric field due to a volume charge distribution in ##V'## plus electric field due to a surface charge distribution in boundary of ##V'##. ##\displaystyle\mathbf{E}=\int_{V'} \dfrac{\rho...
  36. T

    Capacitor and electrostatic field

    Is there any electrostatic field around the leads of a charged capacitor? Let's take just the negative one. If I take a piece of tissue and put close to that terminal it will attract or repel the paper? And if not, why?
  37. CharlieCW

    Conductor sphere floating on a dielectric fluid

    Homework Statement A conductor sphere of radius R without charge is floating half-submerged in a liquid with dielectric constant ##\epsilon_{liquid}=\epsilon## and density ##\rho_l##. The upper air can be considered to have a dielectric constant ##\epsilon_{air}=1##. Now an infinitesimal...
  38. astroman707

    Charged pendulum problem

    Homework Statement A cork ball is suspended at an angle from the vertical of a fixed cork ball below. The mass of the suspended ball is 1.5x10^-4 kg. The length of the suspension thread is .1m. The fixed ball is located .1m directly below the point of suspension of the suspended ball. Assume...
  39. iVenky

    A material containing negative ions is placed between the plates of a charged capacitor

    Homework Statement I have a material placed between parallel plates depleted of free electrons and contain negative ions. What would happen to the charge stored across the plates? Would it still be similar to placing a capacitor with a di-electric constant between them? Homework Equations Q=CV...
  40. C

    Electric field created by a charge seen through an infinite plate (dielectric vs. conducting)

    Having come experimentally to an interesting electrostatic effect, I have returned, aged 47, to my old books in physics. It turns out that my books delight in using Gauss theorem etc. in rather ideal geometrical surface charge distribution, but never gave me the tools to answer to this simple...
  41. Kaan99

    Electrostatic self-force is zero

    Homework Statement Consider a charged body of finite size, (\rho=0 outside a bounded region V). \vec{E} is the electric field produced by the body. Suppose \vec{E} \rightarrow 0 at infinity. Show that the total self-force is zero: \int_V \rho \vec{E} dV = \vec{0}, i.e. the charged body does not...
  42. G

    Potential generated by a point charge in a isotropic medium

    Homework Statement When a point charge is positioned at the origin = 0 in an isotropic material, a separation of charge occurs around it, the Coulomb field of the point charge is screened, and the electrostatic potential takes the form \phi(r) = \frac{A}{r} \exp\left( -\frac{r}{\lambda}...
  43. Javier Lopez

    A Problem with an ion generator

    I have to increase ion generation in a small ion accelerator but I have troubles to go over 20mA (1.27e17 ions/second). I can modulate up to 40 Mhz at 1kV. What ion generator it is recommended gor large ion flux?, I can work in pulse generation.
  44. C

    Finding the potential inside a semiconductor

    Homework Statement My question is more about understanding the task itself, not about calculation. I am supposed to use the poisson equation, to derive the potential inside a semiconductor for a barrier with potential height ##\phi_B## and a donator doping with ##N1 > N2##. Then I should use...
  45. B

    Electric Field and Potential in a conductor

    So in my textbook (Introduction to Electrodynamics by Griffiths) it said that inside a conductor, the electric field E would have to zero, since if it wasn't the free charges would move accordingly and create a electric field that cancels the original field. But in a question that soon followed...
  46. G

    System of multiple conductors: image method

    Homework Statement The following figure represent the traversal cut of a system with two cylindrical equal conductors of radius r0 length l at a distance d from one another and at the same distance h of a plane conductor (conductor zero). The dielectric that surrounds the conductors is the air...
  47. G

    2 definitions for voltage, how are they equivalent?

    So I'm studying electrostatics and I came across to two different definitions of potential difference/voltage (because we're in stationary regimes) and I'm having trouble understanding how the expressions are equivalent. They are for a voltage between point A and point B $$U=V_a - V_b...
  48. J

    I Charged insulator with electrons throughout its volume?

    Could one make a negatively-charged insulator with the extra electrons trapped all the way through its volume by building it up layer by layer with electrons "sprayed" onto each layer as it was constructed? I guess the electrons would be trapped in empty atomic orbitals within the material - is...
  49. C

    Electrical How to maximize the efficiency of the corona discharge generator

    Hi, I have a wirmhurst electrostatic generator and I want to use it to create a corona discharge. My common sense tells me that the metal "shaft", which connects to the metal spheres should lead to significant (electron) leak, since it has a much smaller radius of curvature than said spheres. If...
  50. lordlarddallas

    Potetial Difference between center and point r

    Homework Statement A cylindrical conductor of length L and radius R, L » R, carries a charge Q. 1. Neglecting boundary effects; evaluate the potential difference between a point at distance r from the center of the cylinder, and the center. Assume r to be of the same order of magnitude as R but...
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