New answers tagged electrostatics
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Why does charge distribute itself uniformly only on the surface of spherical conductors?
The below addresses the word "uniformly distributed over the surface"
Solving the Laplacian equation may help.
The spherical conductor is equipotential at the surface, say $V_{0}$
Set the ...
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Faraday's Law - When do we know when it is a motional EMF or an induced electric field?
My question is, how can we differentiate these 2 completely different scenarios from each other? Or are they the same scenarios?
They are different descriptions of the same phenomenon, because they ...
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Can dielectric slab be used to move an object?
In a real system, there will be other forces: things won't just float in space.
The electrostatic force on the dielectric slab is purely attractive, in the direction pulling the slab into the ...
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Infinite electrostatic plate acceleration
On way to do this is make your not-so-infinite plate a charge distribution on a disc (aligned on $z$ for reasons):
$$\rho(r, \theta, \phi) = \sigma (1-\Theta(r-R))\delta(\theta-\frac{\pi} 4)$$
Now you ...
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For electric field between two parallel plate capacitor given by $Q/A*\epsilon_0$, how does the inverse proportionality of area make sense?
The formula that you've quoted applies to a capacitor for which the plates' dimensions are much greater than their separation.
The result follows almost immediately from Gauss's law and symmetry, ...
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For electric field between two parallel plate capacitor given by $Q/A*\epsilon_0$, how does the inverse proportionality of area make sense?
With increasing the area, the capacitance would increase, which you see from $C = \epsilon \frac{A}{d}$.
The question now is whether you apply a voltage that is then constant or if you have a fixed ...
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Why decreasing the distance between a parallel plate capacitor increases the electric field? Wouldn't it remain the same? $\sigma/\epsilon_0 $?
The capacitance has nothing to do with electric field, it is constant for a given capacitor.
Learn more here
https://www.physicskey.com/63/capacitance
Electric field is proportional to charge and also ...
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Why decreasing the distance between a parallel plate capacitor increases the electric field? Wouldn't it remain the same? $\sigma/\epsilon_0 $?
Starting from the expression of the electric field of a 2-dimensional circular charged plate with radius R. The correct expression for the electric field is $$\mathbf{E}(x)=\frac{|\sigma|}{\epsilon_0\...
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Why decreasing the distance between a parallel plate capacitor increases the electric field? Wouldn't it remain the same? $\sigma/\epsilon_0 $?
Two possibilities.
1 Charged capacitor not connected to anything else.
Charge,$q$, and hence charge density, $\sigma = q/A$, cannot change.
Electric field $E = \sigma/\epsilon_0 = V/d$ does not change....
- 93.8k
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Why decreasing the distance between a parallel plate capacitor increases the electric field? Wouldn't it remain the same? $\sigma/\epsilon_0 $?
Assuming a constant potential difference is applied to capacitor, Like battery
Why do you think that The Charge density "sigma" will not change? If you calculate carefully, The electric ...
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Why is the potential due to induced charges constant?
From Gauss's law for the point charge (eq. 3):
$$\nabla^2\phi_{\mathbf y}(\mathbf x) = 2\pi q\cdot\delta(\mathbf x - \mathbf y)$$
This is symmetrical in $\mathbf x$ and $\mathbf y$ since $\delta(\...
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Order of magnitude of $v=\sqrt{q^2/Mr}$
There's several ways to derive classic electron speed in a hydrogen atom, based on simplified Bohr atom model. For example, you can equate Coulomb force work done rotating electron around nuclei to ...
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Theoretical expression for the capacitance of interdigitated electrodes
Okay, it was indeed pretty geometrical. The problem is that in the diagram it is not specified that the width of the horizontal bars is also $w_0$. In that case, in the absence of overlapping, $2l=a-...
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Why do we say that electric potential energy is stored in the electric field?
There are two things to note here:
Electrons are free to move wherever they like to be within any electrical conductor. The steady state is that they do not feel the urge to move at all (ignoring ...
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Why do we say that electric potential energy is stored in the electric field?
If you wiggle charges in the right way, they produce electromagnetic waves. These waves can extend for great lengths. For example, the Voyager space probe is a spacecraft that is headed for deep space....
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Why do we say that electric potential energy is stored in the electric field?
Here is a simple argument that I find suggestive ...
The capacitance of an 'ideal' vacuum-spaced parallel plate capacitor (one for which the plate dimensions are much greater than the plate separation,...
- 34.9k
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Why do we say that electric potential energy is stored in the electric field?
I don't really get why do we say energy is stored in electric field
rather than in the charges upon which we or the battery does work.
It is stored in both. Electrostatic potential energy, just like ...
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Why do we say that electric potential energy is stored in the electric field?
It can be difficult to see why the electric field has to store energy when studying electrostatics alone. Electrodynamics provides the real motivation. As David Griffiths puts in his text Introduction ...
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Apparent flaw in Griffiths EM on solving Laplace's equation
My thoughts on this: I guess it has to do with the fact that the potential function is continuous throughout... Think about it... Had it not been continuous, the electric field in the region/point of ...
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What is the meaning of $\vec H$ with respect to the total field?
Here the problem is that you are using too many notations and you are changing them constantly.
The master equation in electrostatics :
$$ \vec{D}= \epsilon_0 \vec{E} + \vec{P}.$$
(i) $ \vec{D} $ is ...
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Method of image charges for electric potential in a metallic disk
Check out Jackson's Classical Electrodynamics section 3.12 "Mixed Boundary Conditions; Charged Conducting Disc." The method is actually the reverse of the method of images. Usually, the ...
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Applying Gauss law to a current carrying conductor
It applies in all cases as long as you have a closed surface that is
$$\int_S E•da= q_{enc}/\epsilon$$
But is this equation useful in solving the problem? It is if there's sufficient evidence to show ...
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Morphing of Equipotentials of a point charge in a grounded box
You can calculate the potential in this case. You typically have two main methods. Either you expand into basis functions by separation of variables. The basis functions will be of the form:
$$
e_n=\...
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Intuitive charge distribution
Starting from the inner positively charged point charge (assuming point charge for simplicity) and charge neutral but polarized outer shell, when you add negative charge to the outer shell, (0) the ...
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Intuitive charge distribution
"lets say I now add more negative charge to q1 while its in the 2nd state, does the negative charge migrate to the inside surface or remain at the outer surface."
It remains on the outer ...
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In depth answer: Why do I see sparks when I remove synthetic clothes off my body?
The description in your main paragraph is correct. The phenomenon is the triboelectric effect. Dry skin (and dry hair) has an affinity for positive charge, while synthetic fabrics (and plastic) have ...
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Is Faraday's cage described in electrostatic 100% insulated?
Electrostatics problems do not consider cases where charges are moving. They are valid problems, but more complex. So you have one electrostatic problem. You add a charge and wait again for ...
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Potential - metal sphere in a uniform electric field
Yes, but your last equation is valid for all $\theta$. You can use this fact and the orthogonality of the Legendre polynomials to conclude that all the coefficients are zero.
Indeed, for “any” ...
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In an electrostatic field with zero divergence everywhere, where is the charge located?
You can look at the required charge when your field is given by your formula in a finite domain $D$ and zero outside. Physically, this gives you a surface charge on the boundary $\partial D$ given by:
...
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Force between charged hemispherical shells
It turns out that the self force is zero in electrostatics (also true for magnetostatics). You can prove it using the Maxwell stress tensor (generalisation of electrostatic pressure):
$$
f = \nabla\...
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Can two electrons attract each other?
We are currently exploring a hypothesis that suggests two electrons can exhibit attractive forces under certain conditions, specifically when considering their magnetic dipole moments and specific ...
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What happens to the potential energy stored in a capacitor when the plates are pushed closer together?
So, the stored potential energy decreases when the plates are pushed
closer together. Is this correct?
Correct. But the plates don't get "pushed" together, they get pulled together by the ...
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What happens to the potential difference and charge of a capacitor with dielectric if a battery is disconnected?
Why should anything change as there is no conducting path between the two plates?
The "extra" energy stored in the dielectric cannot change unless the dielectric is imperfect and there is a &...
- 93.8k
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Why can't we calculate potential at a particular point due to an infinitely long thin wire with uniform positive linear charge density?
We can definitely calculate the electric potential, as long as we choose a valid (in this case, non-infinity) reference point with respect to which we measure the potential.
The common choice in ...
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Inductor Charging and Discharging
You asked "Inductors discharge in the same direction unlike Capacitors which discharge in the opposite directions. Why?".
Because Capacitors ARE unlike Inductors.
Think of capacitors as ...
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Collection of negatively charged aerosols
Supposing by "aerosols" you mean the particle phase of an aerosol, then yes it can be done and is common practice in aerosol physics, when aiming for particle size distributions of an ...
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Solution to Laplace equation in spherical coordinates and Legendre polyomials
Is there any physical reason that enforces us to use the polynomials instead of the general series solution?
Yes. Legendre functions where $l$ is not an integer diverge at $x=1$ or $x=-1$ or both, ...
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Voltage Difference Across Capacitor Plates
The 9V in "9V battery" typically refers to it's emf, and this would be the potential difference between its ends. Since the potential is defined up to an arbitrary constant, it could mean ...
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Can the formula for a conductor be applied to a grounded infinite conductor plate?
If you're only interested in what's happening on one side of the plate, you may ignore the other side (assuming infinite conductivity). Infinite conductivity forces $\vec{E}=0$ inside the plate, so ...
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What is the equation describing the boundary of a 2D charge density?
Wikipedia gives:
if
$$
\nabla^2u=-f
$$
Then:
$$
u=\int_V d^3 r \, G.f + \oint_S d^2 r\, G_n.g
$$
Where $g$ is the bondary value and $G$ is the Green function. It would seem that solution may be ...
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Electric field inside a uniformly charged insulating sphere
Your reasoning is correct to some degree:
the charge enclosed is evidently 0, which suggests 0 electric field
according to Gauss’s law
One point is missing in your reasoning: Gauss's law tells you ...
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Modeling a pure dipole as a function similar to a Dirac delta function
The (distributional) derivative of the delta function does what you want. By definition,
$$ \int \mathrm dx \ \delta'(x)f(x) = -f'(0)$$
which is motivated by the standard integration by parts formula. ...
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Using method of images on ungrounded spheres
The method of images for a grounded sphere of radius $R$ centred at $z=0$ and a charge $q$ at $z=a$ is given by the image charge
$$q'=-\left(\frac{R}{a}\right)q$$
at $z=R^2/a$. This setup ensures that ...
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Using method of images on ungrounded spheres
In 3D, the electric potential converges to a finite value at infinity (provided the charge distribution is sufficiently localised). Grounding a conductor means that its potential is set to be equal to ...
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Parallel plate capacitor infinite energy
A system's energy, which is conserved when the system is closed, is the sum of the kinetic and potential energy. You've forgot to take the potential energy, namely $\Delta x Eq$, into account.
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Electric field produced by a uniformly polarized sphere
The macroscopic Gauss's Law for $\vec{D}$ is not enough to solve this problem. In a (static) system with the divergence equation $\vec{\nabla}\cdot\vec{E}=0$, you can conclude that $\vec{E}$ is a ...
Buzz♦
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Electric field produced by a uniformly polarized sphere
You don't need to specify the $z$ direction.
To get a uniform polarization in a linear dielectric, you need to immerse it in a uniform external field, $E$, where $E$ is the value far from the field.
...
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Parallel plate capacitor infinite energy
Let's say the capacitor has voltage $V$ and charge $Q = CV$. Let's assume that a positive charge $+q$ and a negative charge $-q$ are created halfway between the plates, with $q\ll Q$ (and equal mass, ...
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Why doesn't an electron rip itself apart?
The simplest answer is: because it's held together by its own gravity. In fact, we could take this one step further: it actually is a gravitational soliton; nothing more, nothing less, and that there ...
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What is the force between two charged objects when the space between them is partially filled by a dielectric medium?
Although in the situation you posted in the question, I get the same result (net force on each charge decreases) but the logic/concept used to solve it was completely different and in a different case ...
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