4 votes
Accepted

Discontinuity in integrand while calculating the electric field of a uniformly charged sphere

The volume factor around the problematic point is is $4\pi |r-r'|^2 d(r-r')$ and the $|r-r'|^2$ cancels against the $1/|r-r'|$ to give a finite integrand.
mike stone's user avatar
  • 52.5k
3 votes

Electric fields created by electrons

The total charge density of proton ($p$) and electron ($e^-$) is given by $$ \rho(\vec{x})= \rho_{ p}(\vec{x})+\rho_{e^-}(\vec{x}),$$ with $$\begin{align}\rho_p(\vec{x})= e\, \delta^{(3)}(\vec{x}) \...
Hyperon's user avatar
  • 4,602
3 votes

Electric displacement field in a conductor

I believe the questions stems from viewing $\vec{E}$ and $\vec{P}$ as independent. But $\vec{P} = \epsilon_0 \chi \vec{E}$ Thus: $\vec{D} = \epsilon_0\vec{E}+\epsilon_0 \chi \vec{E}=\epsilon_0 (1+\chi)...
Daniel's user avatar
  • 266
2 votes
Accepted

Energy of Monochromatic Beam of Light

You've confused several things: Photons. 𝐸beam=𝑁ℏ𝜔, N is an average number. If you measure the number of photons within a given time interval using a photo-multiplier tube, T, then you'll find ...
JQK's user avatar
  • 1,748
2 votes

Graphical interpretation of complex electric fields

This is a notation we use because it makes it much much easier to work with the fields. We just remember that we have to take a real part of the complex quantities to get a real field value. So the ...
BaddDadd's user avatar
  • 310
2 votes
Accepted

Will a charge move if it has electric potential but the field is zero?

What you describe is an unstable equilibrium. A charge exactly at that point will feel no force. But any slight deviation in position from the exact center will produce a small force that accelerates ...
Dale's user avatar
  • 98k
2 votes

Problem with understanding the definition of electric potential

Potential is uniquely defined up to an arbitrary additive constant, so it doesn't matter which starting point you use or the value of the potential at this point. The value of the potential at any ...
Puk's user avatar
  • 13.5k
2 votes

Expectation value of the electric field of a charged particle

In general, the expression of the expectation value of the electric field is: $$<E(r)> = \frac{q}{4\pi\epsilon_0}<\Psi(r)|\frac{1}{r^2}|\Psi(r)>.$$ As can be seen, it depends on the ...
T. ssP's user avatar
  • 513
2 votes

Field outside a hollow conductor

Feynmann is right that no static charge distribution inside a hollow grounded conductor produces any field outside the conductor. As far as Gauss' law goes, because the conductor is grounded, i.e. ...
Albertus Magnus's user avatar
2 votes
Accepted

Surface charge density of a conductor is inversely proportional to radius of curvature: proof?

Charge density isn't proportional to curvature in a charged conductor where the curvature varies. Take a thin cylindrical needle perhaps with spherical ends as an example. Charge will flow until the ...
mmesser314's user avatar
  • 37.9k
2 votes

Charge Inside a conducting hollow sphere

Since the problem's geometry consists of two concentric spheres, one can apply Gauss' law, $$\oint_S \vec E\cdot n\;dA={Q_{enclosed}\over \epsilon_0};$$ to great effect in analyzing the electric field ...
Albertus Magnus's user avatar
1 vote

Potential energy of an electric dipole without any external field

If the dipole is formed from two point charges $q$ and $-q$ a distance $d$ apart it has dipole moment $p=qd$. The potential energy of this system of charges is $$ U=-\frac{q^2}{4\pi\epsilon_0 d} $$ ...
AXensen's user avatar
  • 7,176
1 vote
Accepted

Gauss law does not look right for a flat volume

Very long thin Gaussian surfaces can be quite tricky. The answer will end up being that the small component of the flux going out the sides really does account for the decrease in magnitude coming ...
AXensen's user avatar
  • 7,176
1 vote

How does capacitance of a capacitor not depend on the distance of the capacitor to a battery?

You are correct: the capacitance does depend on the geometry of the wires connecting it. We commonly account for that extra capacitance as a separate "stray capacitance" in parallel with the ...
John Doty's user avatar
  • 20.2k
1 vote

How does capacitance of a capacitor not depend on the distance of the capacitor to a battery?

For a plate configuration of a certain capacitance, C, the charges on the plates are determined just by the value of $C$ and the applied potential difference, $\Delta V$, between the plates. $Q=±C\...
Philip Wood's user avatar
  • 35.4k
1 vote
Accepted

Problem with understanding the definition of electric potential

The electrostatic field is defined as a gradient of a scalar potential: $$\vec E(\vec r)=-\nabla V(\vec r).$$ Thus there is considerable freedom in how one might a scalar potential for any given ...
Albertus Magnus's user avatar
1 vote

Charge Inside a conducting hollow sphere

The electrons in the inner sphere will rearrange themselves so as to shield the inside from any static electric field produced by charges outside it. The electrons in the outer sphere will also do the ...
Brian Bi's user avatar
  • 6,396
1 vote

Charge Inside a conducting hollow sphere

The net electric field inside the inner conductor will be zero. You are correct there. The electric field outside the inner sphere and inside the outer sphere (R1<r<R2) will be non-zero. The ...
Devansh Mittal's user avatar
1 vote

Do electrons move faster towards the end of a circuit?

If that circuit is an accelerator beam pipe, then: yes, that's the point. If it's something with plain old resistance, then they loose $IV\tau = 1\,{\rm J}$ of energy to resistive heating, where tau ...
JEB's user avatar
  • 32.7k
1 vote
Accepted

Sign choice for line element while finding potential due to point charge

Canonical or not, I find the approach you give a bit convoluted. As I see it, the potential, $V(R)$ due to point charge $Q$ at displacement $\mathbf R$ from $Q$ is the amount of work per unit test ...
Philip Wood's user avatar
  • 35.4k
1 vote

Surface charge density of a conductor is inversely proportional to radius of curvature: proof?

For a conducting sphere of radius $r$ and surface charge density $\sigma$ has a potential $V=\dfrac{1}{4\pi\epsilon_0}\dfrac{\sigma 4\pi r^2}{r}= \dfrac{1}{\epsilon_0}(\sigma \,r)$. Thus if the ...
Farcher's user avatar
  • 94.9k
1 vote

Why force by electric field is appearing?

The Lorentz force creates makes for an excess of positive charge at the top (ceiling) of the wire (electrons travel up from the floor to the ceiling of the wire). At equilibrium: Lorentz force pushes ...
Daniel's user avatar
  • 266
1 vote

Solving Maxwell Equations when a charge is put inside a generic conductor

First, I want to note that your description of the situation sounds like it violates charge conversation. You can't just "impress" a charge at a particular location at some time $t_0$ ...
Michael Seifert's user avatar
1 vote

When an electrostatic field is created, doesn't it automatically generate an induced magnetic field?

I was imagining to put a charge in a region of space. First there was no electrostatic field and then it appears, how does it all happen? This is not possible. It would violate the conservation of ...
Dale's user avatar
  • 98k
1 vote
Accepted

How do you express the electric and magnetic field of a TEM uniform plane wave due to a magnetic current density?

If you're talking about the fields generated by a current of magnetic charges, the electric-magnetic duality relation is of use. It says that any solution of Maxwell's equations in vacuum may be ...
Michael Seifert's user avatar
1 vote

Does gravity affects electromagnetic waves? Or electromagnetism affects gravity?

In Newtonian physics, electromagnetism and gravity are distinct entities with no connection. However, in general relativity, there's a bit of a connection to be had. In all physics, mass is ...
Cort Ammon's user avatar
  • 46.8k
1 vote

Why does Gauss' Law apply to any shape given that it's a closed surface?

Gauss' Law is valid for any closed surface, provided that it meets the conditions for forming a "Gaussian surface". However, most textbooks derive this equation using a sphere because it ...
rania h's user avatar
  • 11

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