What is Electrostatics: Definition and 679 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.
I derived an expression for the electric field due to solid uniformly charged non conducting spherical volume to be
$$ \frac{ Qz} {4π\epsilon R^3 } $$ where z is the distance of the point from the center and it is less than the radius R I.e the point lies inside the sphere...
This in terms of...
This is the direction of the electrostatic force on each element due to the charge kept in the center of the ring.
According to me tension in each element of the charged ring should be balancing each of these forces...so its pointing radially inwards
But I know I am wrong because the...
So I know I have to equate force on a hemispherical shell with spring force to get value of compression but I can't find the force on the hemispheres
Some places that do have the solution use the formula :
$$\text{Field of non-conducting hemispherical shell= } \frac{\sigma}{2\epsilon_○} $$
This...
Following the above statement my teacher was trying to prove something and it started with suppose q1 and q2 are charges placed in a medium (k) of infinite expanse. The distance between them being r. He took q1 and q2 to be some spherical particles and not point charges and concluded that
Net...
I’ve been trying to get the proper understanding of electric field. Fine I get the definition: any charge changes space around itself and thus generates electric field that acts with force on any object that’s relatively close to the charge.
But first from the first, how can the FIELD act with...
So from Gauss theorem, electric field at any point inside a uniformly charged sphereical shell is zero. Thus there is no electrostatic force on the inner sphere.
From what I have learnt, a field is necessary to move charges. But in this case the inner sphere acquires a charge q without any...
I have read Griffiths' Chapter 2 sections on Conductors. According to it, (if I understood it correctly) if the charge is put inside the cavity of a conductor, then the equal and opposite total charge will be induced surrounding the cavity. This charge and the total charge induced surrounding...
I'm using a cylindrical gaussian surface that is right inside the positively charged conducting plate and has the other end in-between both plates. I'm having trouble discerning whether the charge density(##q_{in}##) should be ##\frac{\sigma}{2 \epsilon_0}## since the cylinder is only...
We have
$$\vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}\int_V\frac{\rho(\vec{r}')}{\eta^2}\hat{\eta}d\tau'\tag{1}$$
A few initial observations
1) I am using notation from the book Introduction to Electrodynamics by Griffiths. When considering point charges, this notation uses position vectors...
This is the picture of the problem. I attach my solution.
I first used a trick with gauss's law to calculate the radial electric field at first order of r. ( where r is small ) ( we can assume ##small r=\delta r##) I used a cylinder at the center of the ring then i calculated the ##\hat{z}##...
Often in potential calculus problems, the uniqueness theorem of the solution of the Poisson problem with Dirichlet and Neumann boundary conditions is improperly "invoked," without bothering too much about making such an application rigorous, i.e., showing that indeed the problem we are solving...
Hah! You thought this had to do with experimentally testing the Schrodinger cat scenario? Nope.
Some may know that a good way to concentrate radon daughters is to rub a balloon and let it sit for a while to attract charged aerosols. Without fail, all physics demos appear to call for cat's fur...
I have several questions relating to electrostatics:
first of all, in this derivation for the formula of the electric potential energy:
work is being done against the electric field right, so the work should be negative, but in this case it's positive. I'm wondering if it's because the direction...
The model that he uses is a dielectric in which there is a spherical cavity with a dipole at its center. The dipole ##\vec{m}## has a component due to a permanent dipole and a component due to an induced dipole (because of polarization).
In order to obtain the dipole moment in the cavity, the...
TL;DR Summary: Independence of potential( inside a rectangular pipe running along z axis)from z coordinate
Consider the following diagram
It is an infinite rectangular pipe running along z axis.I know that the potential inside the pipe is independent of z coordinate, but I cannot seem to...
A capacitor consisting of 2 square metal plates placed at a certain distance is connected to a potential difference generator V.
A slab of dielectric material is inserted into the space between the armatures.
By doing the calculation of the derivative of the electrostatic energy with respect...
I think definition (a) is not correct since the center of charge distribution rather than mass distribution is important here. The correct definition is the one given in (b).
I am thinking that a distribution of charge will have a center of charge ##(x_c,y_c,z_c)## for -ve charges according to...
Problem:
Solution:
When I looked at an example problem, they started writing the potential in terms of the Legendre polynomials.
The example problem:
This is what I did:
$$V_0 \alpha P_2 (\cos(\theta)) \Rightarrow \frac{\alpha 3 \cos ^2 (\theta)}{2} - \frac{\alpha}{2} \Rightarrow \frac{\alpha...
The electric field strength at the center of a uniformly charged disk should be zero according to symmetry of concentric rings about the center, where each ring is contributing to the electric field at the center of the disk.
For a thin ring of uniform charge distribution the formula is ##E =...
Doing so, we can consider the balloon to be a point charge (approximately). Can we do it in this case, when there are only electrons on its surface? Or is it stupid and we can't do it under any circumstances?
Since the forces involved (gravity and electric force) are conservative we can use conservation of energy.
The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
I have wrote all feilds and potentials and I want to find the constants.
My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ?
Second one is " when I want to write the gausses law for the point x=a I...
Hi wizards,
I'm working through Jackson's book on E&M (3rd edition) and got stuck in section 3.12 on expansions of Green functions. I have three questions regarding section 3.12:
First, why is Jackson trying to find a Green function that satisfies equation 3.156? To my beginner mind, it...
If I want to calculate the dipole moment of a dielectric cylinder of uniform polarization perpendicular to its axis, I could multiply the polarization by the volume of the cylinder, which is okay. But another method is to consider the cylinder to be a superposition of two cylinders of equal and...
Does the second uniqueness theorem just say that if there is an electric field that satisfies Gauss's law for a surface surrounding each conductor + a surface enclosing all the conductors, it is indeed the true electric field, and no other electric field will satisfy those conditions?
in this example in Griffiths' electrodynamics, he says the following :(Figure 3.7 shows
a simple electrostatic configuration, consisting of four conductors with charges
±Q, situated so that the plusses are near the minuses. It all looks very comfort-
able. Now, what happens if we join them in...
1)Field Lines is supposed to represent the electric field around a charge ,now we can draw infinite field lines around a charge and sinc Electric flux is No of Field Lines /area ,does it become infinite ,the whole concept of field lines is quite in the Gray Area for me ,I can in theory mark...
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...
Hi all ,
please refer to the picture regarding my working.
please correct me if My working is wrong.
I am quite confused about the positive and negative sign in equation
I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help.
The torque on a dipole can be defined as
τ=PEsinθ
The work done on a dipole to move it from an angle ##\theta_0##...
From the second equation I get that,
##\vec D =\frac{q}{4\pi \vec r^2}\hat r##
From first equation I get that
##\vec E = \frac{q}{4\pi \vec r^2 \epsilon}=\frac{q}{4\pi \vec r^2 K \epsilon_0}##
But I saw that the answer is ##\vec E=\frac{\vec E_0}{K}##
While writing the comment my mind said...
Summary:: I been stuck on this problem from past 4 months. I am completely done. I am getting no idea. Even my professor couldn't have helped me. Can anyone please help me? 😔
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...
(a) Knowing ##E##, we can use equation (2) to determine ##V##. However, since ##\vec E## represents the distribution of electric field in space i.e. a function of (x,y,z). For example, ##\vec E = x \hat i + y \hat j + z \hat k##. Here we do not know this function so how can we know ##V## at a...
Hello, any answers appreciated:
'Two spheres are 5 m apart. Sphere 1 has a charge of -20 mC and sphere two has a charge of -50 mC. (a) Find the strength of the electric field at the sphere's halfway point. (b) Find the electric potential at the halfway point
If the book had said that electrical potential energy is the negative of work done by electrical force on a charge, then the definition would be very clear and easy to understand. So, why should the book give this confusing definition instead.
I have tried to understand the solution given in the book which is as pasted below. The solution uses Gauss's Law but makes no mention of which Gaussian surface is used. The diagram that I have used to understand this problem is also given at the end. From the diagram, faces OADG, OABE and OEFG...
First I did drho/dr which is equal to 35.4*10^-12/R. Then I integrated drho by which I got rho=35.4*10^-12. And then the last eqn will be q=rhoV. But the answer was wrong.
I have a doubt on the formula I am using for E because that formula is for a point charge or a charged shell.
delta q=rho deltaV
rho=dq/dV
dq=rho4pir^2dr
Then integrate dq from 0 to a because A is to be uniform in shell.
Ans: A= 5.3*10^-11 C/m^2
How do we approach these problems? Looking at the answer A seems to be surface charge density. What is A? What is the direction of uniform field E. I don’t...
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...
Gauss law relates the net flux phi of an electric field through a closed surface to the net charge q that is enclosed by that surface. It tells us that
Phi = q/permittivity
Can I say it like this : The gauss law states that the net flux of the surface depends upon the net charge enclosed by that...
When I look at this question, I can see two possible values of electric flux depending on how I take the normal area vector for either ends ##A \text{ and } A^{'}##.
What is wrong with my logic below where I am ending up with two possible answers? The book mentions that only ##2E\Delta{S}## is...
(a) Due to Coulomb's law all charges whether internal or external to Gaussian surface will contribute to the electric field. This is also mentioned as it's correct answer.
(b) The answer is "equal to", which makes no sense to me. It could be greater than, equal to, or less than that obtained...
According to a popular book on electrodynamics a special case of electrostatics is- ''source charges are stationary (though the test charge may be moving)''.
My question is- now that the test charge is moving, how is it a special case of electrostatics anymore?
Also many times we deal with...