What is Electrostatic: Definition and 874 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.
This is SAMPLE PROBLEM 25-7 from "Physics" by Resnik, Halliday, and Krane, in the chapter "Electric Field and Coulomb's Law".
After describing the behavior of uniformly charged spherical shells:
follows a sample problem:
The solution to (a) goes to say that the volume inside R/2 is 1/8 of the...
The answer to the first question should be a sphere since for very large distances the multiple charges will act as a point charge. 1(a) is correct answer.
For the second question, I find it slightly vague. How can equipotential surface be zero, may be it's asking for the potential of...
Problem:
I have done part a) in spherical polar coordinates.
For part b) I thought it would be just:
$$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$
But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...
The correct answer to this problem is: ##\sigma = \varepsilon_0E\frac{\varepsilon-1}{\varepsilon}##
Here is my attempt to solve it, please tell me what is my mistake?
##E_{in} = E_{out} - E_{ind}##
##E_{ind} = E_{out} - E_{in}##
##E_{in} = \frac{E_{out}}{\varepsilon}##
##E_{ind} = E_{out} -...
If these point charges were placed in vacuum without any spherical shells in the picture, then the force between these charges would be ##F =\dfrac { k q_1 q_2} {d^2}##.
But, I am unable to reason how spherical shells would alter the force between them.
I do know that if charges were on the...
This is a tricky and difficult question for me. I know from reading various textbooks that electric lines of force are always continuous without breaks, but cannot pinpoint a reason for this.
The only reason I can come up is that an electric line of force must always begin and end on charges...
Part (a) was simple, after applying
$$Q=\int_{\mathbb{R}^3}^{}\rho \, d^3\mathbf{r}$$
I found that the total charge of the configuration was zero.
Part (b) is where the difficulties arise for me. I applied
$$V(\mathbf{r})=\frac{1}{4\pi \epsilon _0}\int_{\Gamma }^{}\frac{\rho...
I solved laplacian equation. and got the solution of V(r, phi) = a. +b.lnr + (summation) an r^n sin(n phi +alpha n ) + (summation) bn r ^-n sin( n phi +beta n)
I get step 1, in which due to electrostatic induction the top part of electroscope gets positively charged while the leaves of electroscope become negatively charged.
Now if we Earth the positively charged end of electroscope as shown in step 2, then electrons must flow from Earth to...
According to Helmholtz’s theorem, if electric charge density goes to to zero as r goes to infinity faster than 1/r^2 I'm able to construct an electrostatic potential function using the usual integral over the source, yet I don't understand how this applies to a chunk of charge in some region of...
I read this paper and this is iindeed a very interesting hypothesis. The implications of this theory if true are enormous! Please comment!
Is Gravity Just the Electrostatic Force?
<crackpot link deleted>
The idea is to wrap a balloon in several layers of material, similar to that used in electrostatic adhesion wall climbing robots, and run power through the layers. The electrostatic charge on the layers outside the balloon will build up and the air inside the balloon will begin to become...
this formula in the picture is the average electrostatic field over a spherical volume of radius R. It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q.
My question is...
If I have a physical dipole with dipole moment p. Now, this formula for potential (V) is a good approximation when r is much larger than both r1 and r2 in the picture below. It's however said that for a pure dipole for which the separation between charges goes to zero and q goes to infinity, the...
The energy stored in a capacitor is derived by integrated the work needed to move charge dQ from one plate to another. I'm confused on how this energy is the same as electrostatic potential energy, the energy needed to assemble this configuration from infinity. In the case of capacitor energy...
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...
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...
As you know, "in the classics" the charges of the capacitor plates are equal in absolute value and opposite in sign. However, let us consider a series connection of capacitors. In this case, a charge of the opposite sign is induced on every second plate of each capacitor due to electrostatic...
Hi,
I am doing e-field simulations and have came across two types; electrostatic and dc conduction. I know that electrostatic means there is no changing field so I'm just hoping for discussion on when one is more appropriate than the other and when one definitely should or should not be used.
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'...
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 weird because if we do that the net force will be equal to 0 and the charge will not move can...
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...
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...
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...
So I started with b)
and it there was no q2 this would seem reasonable
I was wanted to ask , what effect does q2 have on potential of these two charges? Because it has to be given for a reason.
I wonder if you could help me with both I'm stuck, I know that in order to see if the electrostatic equilibrium is stable or not at the center of the ring , the potential energy has to be minimum there. I was going to use Laplace eq. but it allows neither minimum nor maximum. Then I also...
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...
Hi!
I tried to solve it by using the equation of the electric potential above and as we see it requires the electric field, but the electric field at the center of the ring is zero. Then I tried by using the equation [text] V = \frac{1}{4\pi\epsilon_0r} \int \lamda dl [\text] and I got [text] V...
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...
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...
Hello,
If I understand it correctly, the samples are grounded inside a scanning electron microscope (SEM) to avoid charge build up through the electron beam. Also the non-conductive are coated with a conductive layer, so they can be grounded as well.
However, I do not know how the charge build...
For a case of electrostatic field (B is equal zero), how should the force acting on a moving charge be calculated if we want to take into account all the relativistic effects? Also would it be correct to calculate the acceleration of the charge as a=F/m, or should some other formula be used? For...
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...
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...
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...
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...
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I tried just calculating the force with Coulomb's law, then calculating the forces for each vector individually and adding, but I got it wrong both ways
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}$$...
Electrostatic energy involves a volume integral and a surface integral
The question is how to apply this formula to a finite space in which case the 1st term (surface integral) won't vanish. Let's apply to a capacitor and enclose the capacitor by a closed surface. Calculate the energy integral...
I tried to do a Euler Lagrange equation to our Lagrangian:
$$\frac{S_\text{eff}}{T}=\int d^6x\left[(\nabla \phi)^2+(\nabla \sigma)^2+\lambda\sigma (\nabla \phi)^2\right]+\frac{S_{p.p}}{T}$$
and then I would like to solve the equation using perturbation theory when ##Q## or somehow...
I used the concept of electrostatic induction, which would cause the charges in metal ball near the ebonite rod to have +ve charges on end next to rod and a -ve charge on the end touching the other ball.
What confuses me is how charges separate on the second ball. The only way these balls can...
I am trying to check if an expression is dimensionless. If it is, then I have done things correctly. However, I am stuck on how to deal with a (Debye^2) term. How can I break it down to find out if it cancels out with the other units I have left? I know this is probably a trivial question...
We know that both the interior and the surface of an electrostatically balanced conductor are equipotential. My question is if when we approach the loaded objects, the surface of the conductor will continue to be an equipotential. If not, then there could be a field line that left the region...
So it seems the typical way to approach this problem is to consider the sphere when it has charge q and radius r. With uniform charge density ##\rho##, this becomes ##q = 4/3 \pi r^3 \rho## and so ##dq = 4 \pi r^2 dr \rho##. Using our expression for the potential outside of the sphere, we find...
Summary:: If you rub against each other two sheets of paper, one of which contains text, they become
electrified. The electrical pattern that is formed on the clear sheet may be analyzed later to
restore the text, depending on the way the text was created. Propose and build a setup to recover...
I have noticed that F = -dU/dx in gravitation gives the attractive force experienced by both bodies.
For capacitors, does F = -dU/dx give the force experienced by each capacitor?
We all know that Poissson's equation in electrostatic is:
$$\nabla^2\phi=-\frac{\rho}{\epsilon_0}$$
My question is: why the solution, let's say for 1D, is not just double integral as follows:
$$\phi=\iint -\frac{\rho}{\epsilon_0} d^2x$$
which gives x square relation. But the actual solution...