All Questions
Tagged with electric-fields potential-energy
142
questions
1
vote
1
answer
122
views
The (electrostatic) force on an extended object
It is well known that, if I have a system of $N$ particles acted upon only by conservative internal and external forces, then I can obtain the force on the $\mathrm{i^{th}}$ particle as
$$\textbf{F}_i ...
- 1,095
3
votes
1
answer
376
views
Coulomb force from a variational principle
See the attached discussion from Zangwill's Modern Electrodynamics, and in particular footnote 9. The point of this question is to understand how to recover Coulomb’s force law from an assumed form ...
- 1,095
1
vote
3
answers
2k
views
Can electric potential energy be nonzero when the electric field is zero?
I read on wikipedia that electric potential energy of a point charge in the presence of n point charges can be calculated from this formula:
$$
U = k_eq \sum_{i=1}^{n} \frac{Q_i}{r_i}
$$
However, ...
- 23
2
votes
0
answers
160
views
What should the electrostatic energy of a continuous charge density be?
Hope this doesn't come off as too pedantic or overinterpreted. I've been working on revisiting electrostatic and electrodynamic energy from first principles, and I have the following stumbling block. ...
- 1,043
0
votes
1
answer
41
views
A question on the work done by the electric field? [closed]
It's a well-known fact that the work done by the electric field is given by
$\int -k\frac{{Q(1)Q(2)}}{r^2} dr = \frac{kQ(1)Q(2)}r$
The work being negative as the force and direction of displacement ...
1
vote
1
answer
89
views
Energy in electric field of an isolated particle?
I learnt that the energy density of electric field is $\frac{\epsilon_0}2E^2$. However, I'm little confused about how can there be energy associated with an electron in empty space.
How can we have ...
- 23
0
votes
2
answers
438
views
Distribution of interaction energy in electrostatic systems
If we have two electrostatic systems their interaction energy is given by
$$U=\epsilon_0\int\vec E_1\cdot\vec E_2dV\equiv\int\rho_1\phi_2dV\equiv\int\rho_2\phi_1dV$$ Here the integral is over the ...
1
vote
3
answers
398
views
Deriving energy in Dielectrics
Note: I am working in the Lorentz-Heaviside system and all the integrals are over the whole space.
Definitions:
$$\vec E= \vec E_f+\vec E_b$$
$$\phi=\phi_f+\phi_b$$
$$\vec D=\vec E+\vec P$$
$$\rho=\...
0
votes
1
answer
73
views
Disagreements in derivations of electrostatics
In the derivation of the potential energy of electrostatic systems we get (I am working in cgs)
$$W=\frac12\int\phi\,dq=\frac12\iiint\phi\rho\,d V \tag{1}$$ But $$\vec\nabla\cdot\vec E=4\pi\rho$$ Thus
...
3
votes
4
answers
282
views
Consistency of existence of point charges and energy in fields
In Feynman lectures, Volume 2 chapter 8 (https://www.feynmanlectures.caltech.edu/II_08.html#Ch1-audio) at the very end Feynman remarks
We must conclude that the idea of locating the energy in the ...
31
votes
10
answers
8k
views
How is energy "stored in an electric field"?
My physics teacher told me the statement "The energy of a capacitor is stored in its electric field".
Now this confuses me a bit. I understand the energy of a capacitor as a result of the ...
- 492
4
votes
1
answer
359
views
What does negative electrical energy signify?
When we derive the formula for potential energy caused by the torque of a dipole in uniform electrical field we get $U = -pE \cos \theta$. And my textbook tells me that the when the dipole is kept ...
0
votes
1
answer
155
views
Does electric current flow from higher potential to lower potential or from higher potential energy to lower potential energy?
Here, $O$ is a field charge with a $+T$ charge. $A$ and $B$ are test charges with $+T_1$ and $+T_2$ charge, and they are fixed in place. Suppose the points at which $A$ and $B$ are situated are $P_1$ ...
- 1,018
0
votes
2
answers
411
views
Is energy infinite in an electric field?
Energy is defined as the capacity to do work. Work in turn is defined as force x displacement.
An electric field exerts the field in all directions infinitely (even though the strength of that force ...
- 11
0
votes
0
answers
20
views
Using Variation of Energy for a Dielectric to define the Electric Field
I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
- 1