Electrostatics is concerned with the field and potential of stationary electrical charges and electric charge distributions. Problems are this type are almost exclusively concerned with mathematics of geometries using the inverse-square law.

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Applying Gauss' Law to find Electric Field

I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the ...
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62 views

What happens to this energy of the capacitor?

Let's say you have a charged, isolated parallel plate capacitor with a certain voltage. My book says that if you insert a dielectric, the voltage drops. However, that would require the energy between ...
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382 views

Electrostatic induction

Is this a correct definition of electrostatic induction, The production of opposite charges on a neutral body when a charged body is brought near to it? I think it's not the production but ...
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4answers
217 views

Capacitance of a capacitor

Why does the capacitance of a capacitor increase if the distance between the two plates of a parallel plate capacitor is decreased? I think, with decreasing distance between the two plates, the force ...
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336 views

Electric field of a negative charge

Displacing something against the gravitational field, gains it potential energy. Moving something against the nature requires work. If the electric field of a negative source charge 'Q' points inward, ...
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4k views

Electric field of a negative charge

How was it discovered that the electric field of a negative charge points towards the charge itself? Is it true? (Courtesy of wikipedia)
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170 views

Electric potential of a spheroidal gaussian

I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form $$ ...
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74 views

Electrostatic potential and charge

Say we have a balloon, negatively charged, the voltage on it is 500 V. Can I measure the charge on it or in other words, the number of excess electrons?
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151 views

How to check units?

I've got: $Q=\frac{Er^2}{k}$ how to check the units? I start with $\left[\frac{\text V}{\text m} \, \text m^2\right]$, tried replacing $[ \text V ]$ with $\left[ \frac{\text J}{\text C} \right]$, but ...
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76 views

Electric charge and the distance

The strength of an electric field is: $E = 200\ \mathrm{N/C}$ The potential (of the test charge) is: $V = 600\ \mathrm{V}$ $\epsilon_r=1$ I need to calculate the distance between this point and the ...
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2k views

Electric field due to nonconducting sphere

For calculating electric field outside a nonconducting sphere with a hollow spherical cavity. When I use the rule (Charge density= $dQ/dV$), I don't know exactly what is $dV$, is the volume here ...
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146 views

Should the electric potential of a positively charged sphere be negative?

Because the indefinite integral of the electric field results in a negative value? (As the function is proportional to $r^{-2}$? I've got to be missing something... Help please!! Thanks! Also, I ...
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710 views

Potential due to a spherical surface charge

The potential at the surface of an insulating sphere (radius R) is given by $$V(R,\theta) = k \cos(3\theta)$$ where $k$ is a constant. Use separation of variables to find the potential inside the ...
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Finding final charge distribution on capacitors on grounding

I am trying to solve the following problem on capacitors: Here's the circuit I have to find the total energy loss when all three switches are closed, and subsequent equilibrium attained. I had ...
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757 views

Force between two charged rods?

Suppose that we have two rods of length $l_1, l_2$ connected at one end but free to rotate. These rods have charge density $\lambda$ uniformly distributed, so the total charge of rod $i$ is $\lambda ...
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519 views

Potential Inside Conducting Cube

A cubical box with sides of length L consists of six metal plates. Five sides of the box { the plates at $x=0, x=L, y=0, y=L, z=0$ - are grounded. The top of the box (at z = L) is made of a separate ...
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What happens to this potential energy?

Let's say I turn on a Van de Graaff which creates a large positive charge. Now let's say I have an object with a positive charge in my hand and I start walking toward the Van de Graaff from $x$ meters ...
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104 views

Charging an object by induction

when charging a sphere by induction using a (-) charged object , and we put it to the right side of the sphere, electrons are pushed to the left side , so we ground the left side and the excess ...
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How to positively charge an object with a power source? [duplicate]

How do you positively charge something consistently? By what mechanism could this be achieved?
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152 views

electrical forces of two charges repelling each other

If I place two positive charges of different magnitudes on the x-axis (one at the origin, one at the some position x), as the two charges repel each other are the forces that they impart on each other ...
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383 views

distance of electron from proton

An electron is projected, with an initial speed of $1.10 \times 10^5 \text{m/s}$, directly towards a proton that is essentially at rest. If the electron is initially a great distance from the ...
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Using photons to explain electrostatic force

I am trying to understand the idea of a force carrier with the following example. Let's say there are two charges $A$ and $B$ that are a fixed distance from each other. What is causing the force on ...
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1answer
2k views

Gradient of the electric potential

I was wondering if for a point-like charged object, does the gradient of the electric potential point in the direction of maximum increase or maximum decrease of the function $V$?
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532 views

Electric potential at a point outside a charged sphere

The question asked me to find the potential at a distance $r$ from the center of a charged sphere, where $r>r_0$ of the sphere. Actually, the question is answered, but what is confusing me is ...
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240 views

The field of uniformly charged ball (without Gauss theorem)

The solution of Poisson equation is given by $$ \mathbf E = \int \frac{\rho (\mathbf r )(\mathbf r_{0} - \mathbf r )}{|\mathbf r_{0} - \mathbf r|^{3}}d^{3}\mathbf r. $$ I tried to use this term for a ...
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527 views

Electric lines of force

Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so?
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3answers
829 views

Maxwell Stress Tensor in the absence of a magnetic field

I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia, Start with Lorentz force: $$\mathbf{F} = ...
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368 views

Explanation on the resulting forces of two positive point charges

Why will the resulting force lines of two positive point charges be like this: I would expect this:
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Is voltage electric potential or electric potential difference?

On Wikipedia, voltage is defined to be the electric potential difference. However, I am still not certain as to whether voltage is the electric potential ($PE/q$) or electric potential change ...
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How does positive charge spread out in conductors?

I know that when there are excess positive charges in a conductor, for example, a metal sphere, the positive charges will spread out over its surface. However, I am confused about how this excess ...
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123 views

How to make a nongrounded conductor have equipotential?

I'm studying the Method of Images and I seemed to have come to a conundrum. Method of Images takes advantage of grounded objects, (I am currently studying spheres), to set boundary conditions. ...
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117 views

Electric force on spherical surface

I have a doubt about electrical forces on surfaces, for instance, on the surface of a sphere. I'll explain my point: let's say we have some spherical surface of unit radius and there's one point ...
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4answers
3k views

Why is electric potential scalar?

I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional ...
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296 views

Electric field singularities

Is this the list of all possible types of singularities in electrostatic field $E$? near a point charge: $\frac{1}{r^2}$ near a line of charge: $\frac{1}{r}$ near the edge (not surface) of a ...
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68 views

Semi-conductors and induced charge

Can a semi-conductor ( germanium or silicon) or a semi-metal ( graphite ) carry an induced charge ?
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895 views

Why can we use Gauss' law to compute electric field?

For simplicity I'm considering only the sphere case. In the Gauss' Law formulation we have some field $E$ introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get ...
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Ionized Depletion Region, Why aren't those charged being excited?

Ok so I understand the PN junction, and how when 2 Semiconductor materials are placed together the Electrons will jump into the Holes near the junction creating a Negatively Ionized Atoms on the ...
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253 views

Finding the electric field on a point (x,y,z) using Coulomb's Law

Using Gauss' Law, the answer is $$\frac{Q}{4 \pi \epsilon R^2}.$$ However if I were to do the integration using Coulomb's Law, I get $$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR ...
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76 views

Permanently charging a sphere by induction using a high voltage

I want to charge a sphere using a van de graff generator , it would sound easy , but using a 1 MV or a 900 KV is really hard, it is enough to break like 1 meter of air so whenever i try to ground the ...
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104 views

Electric field singularity

What's a general proof for the log-singularity of electric field near the edge of a uniformly charged surface?
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349 views

Electric field lines

If electric field lines cannot terminate in empty space, in the simple example of two equal charges what happens to the line starting from one of the charges toward the other in the middle?
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64 views

numerical investigation of stability [closed]

I am trying to find the required specifications of an paul RF trap, in which a proton can be confined.(trap dimensions,voltage frequency and amplitude used, etc). I have to solve the equations of ...
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60 views

Grounding insulative material

When grounded, can an insulative material keep its charge for any measurable length of time? Or, I suppose, if it was a perfect insulator, would it discharge at all? An example might be a charged ...
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269 views

How do we make symmetry assumptions rigorous?

I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
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520 views

Finding the electric field

The charge per unit length on a long, straight filament is -91.9 µC/m. (a) Find the electric field 10.0 cm from the filament, where distances are measured perpendicular to the length of the ...
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Dirichlet and Neumann Boundary condition: physical example

Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region? If we have a cylindrical ...
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1answer
208 views

Electric Flux Contradiction

I am currently reading about electric flux; and from this passage I am reading, I am sensing a bit of a contradiction: "If the E-field is not perpendicular to the surface area, then the flux will be ...
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1answer
175 views

Electrostatic charge leakage

What are the ways electrostatic charged objects leak charge in humid conditions? Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a ...
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1answer
1k views

Minimizing potential energy of a dipole in an electric field

My test paper asked me which way a dipole should be orientated in an electric field to minimize its potential energy. My answer was that the dipole should lie parallel to the electric field with the ...
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2answers
487 views

Calculate force of electric charges “suspended” by strings [closed]

In a question: Two small plastic balls hang from threads of negligible mass. Each ball has a mass of 0.110g and a charge of magnitude q. The balls are attracted to each other, and the ...