All Questions
11
questions
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On generalised potential in Electrodynamics
I'm studying Lagrangian Mechanics from Goldstein's Classical Mechanics. My question concerns Section 1.5 which talks about velocity-dependent potentials.
I am actually unsure about how Equation 1-64' ...
- 1,638
0
votes
2
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102
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How to understand "the potential energy in an EM field is determined by $\phi$ alone"?
Goldstein page 342,
Consider a single particle (non-relativisitic) of mass $m$ and charge $q$ moving in an electromagnetic field.
The Lagrangian is
$$ L = T-V = \frac{1}{2}mv^2-q\phi +q\vec{A}\cdot \...
- 1
1
vote
1
answer
122
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The (electrostatic) force on an extended object
It is well known that, if I have a system of $N$ particles acted upon only by conservative internal and external forces, then I can obtain the force on the $\mathrm{i^{th}}$ particle as
$$\textbf{F}_i ...
- 1,095
0
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2
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215
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If Electric potential energy is not zero at infinity, nor at any finite value, when it is?
The electric force decreases with the distance ($1/r^2$). If that's so, if we don't define zero to be in any finite distance value, nor at the infinity, there's just no zero reference at all for the ...
- 169
0
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1
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157
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Follow-up on "Derivation of Lagrangian of electromagnetic field from Lorentz force"
I have a follow-up on this post. The way I understand it, if one generally has a velocity-dependent potential $U(q, \dot q, t)$, then we can derive/define a generalized force $$Q_k = \frac{d}{dt}\frac{...
user248824
1
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2
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749
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Velocity-dependent potentials and the dissipation function
From this previous question Charge, velocity-dependent potentials and Lagrangian where the citation is shown at the page 22, §1.5 of the book Classical Mechanics of Goldstein, we read that
"an ...
- 2,547
0
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2
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233
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Potential energy of a charge in a magnetic quadrupole field
I have a charged particle of charge $q$ that moves with velocity $\vec{V}$ from a position $\vec{r}$, inside a magnetic quadrupole field of the form: $$\vec{B}=B_{0}(x,y, -2z)$$
The Lorentz force acts ...
- 103
1
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0
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527
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Particle in electromagnetic field Lagrangian
Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
- 141
8
votes
3
answers
891
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Coincidence, purposeful definition, or something else in formulas for energy
In the small amount of physics that I have learned thus far, there seems to be a (possibly superficial pattern) that I have been wondering about.
The formula for the kinetic energy of a moving ...
3
votes
2
answers
3k
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Charge, velocity-dependent potentials and Lagrangian
Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
- 1,133
0
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1
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284
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Violation of conservation of energy and potential energy between objects
I would like to clarify my question. I have numbered them to be independent questions
For any conservative fields, $\vec{F} = -\nabla U$. Which means the restoring force is opposite to the increasing ...
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