All Questions
12
questions
0
votes
1
answer
78
views
The magnetic force is conservative when the magnetic field is static, what is its potential function then?
The magnetic force $\vec{F}$ can be conservative when the magnetic field is a static. That is $\vec{\nabla} \times \vec{F}=0$, so it follows that there is a scalar function $f$ such that $\vec{F}=q \...
- 959
0
votes
1
answer
97
views
Lorentz force from potential- extra term?
I'm trying to verify the E.M potential energy $U= \int{A_\mu J^\mu} = q(\phi - A_j v^j )$ by using the connection:
$$
F= - \frac{\partial U}{\partial r} + \frac{d}{dt} \frac{\partial U}{\partial v}
$$...
- 2,142
0
votes
1
answer
156
views
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 $$Q_k = \frac{d}{dt}\frac{...
user248824
1
vote
0
answers
27
views
How can I find the potential energy and force between a steel sphere and a magnet?
I'm fine with certain simplifying assumptions being made, I currently only know high-school level physics (the simpler the better). Also, if anyone can explain the intuition behind formulae, I would ...
1
vote
2
answers
59
views
Regarding the definition of the electrical potential energy
Let us say we have two charge positive $q_{1}$ and $q_{2}$ very far away from each other. Suppose also that $q_{1}$ is stuck in its place. If we want to bring them closer to some distance $b$ apart, ...
- 1,292
0
votes
0
answers
117
views
From Lagrangian of Electromagnetic field to the Lorentz force? [duplicate]
The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force
$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$
and ...
- 1,757
0
votes
1
answer
2k
views
Lorentz force in terms of potential
The Wikipedia page on the Lorentz force states the following:
$$\boldsymbol{F}=q\left[- \boldsymbol{\nabla}(\phi-\boldsymbol{v} \cdot \boldsymbol{A})-\frac{d\boldsymbol{A}}{dt}\right]$$
which ...
- 391
0
votes
3
answers
8k
views
Relationship between Potential and Potential energy
I know that if we have a conservative force then:
$\vec{F}(r)=-\vec{\nabla}V(r)$ where $V(r)$ is the potential.
I also know that I can take potential energy from here doing: $E_{pot} (r) = \int_{S} \...
- 33
2
votes
1
answer
299
views
Is the Potential Energy just a bookkeeping device?
It is said that if the space is homogeneous then momentum is conserved. But I've been thinking in the following situation:
Consider a parallel plates capacitor. In between the plates there is a ...
user115652
0
votes
1
answer
829
views
Understanding the relationship between electric energy and force
I'm trying to do the following problem:
One of the three types of radioactive decay is "β decay", during which protons decay into neutrons or viceversa, emitting either electrons (β) or positrons (...
- 125
5
votes
2
answers
3k
views
Deriving the Lorentz force from velocity dependent potential
We can achieve a simplified version of the Lorentz force by
$$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$
where $\mathbf{A}$ is the magnetic vector potential and ...
- 539
10
votes
1
answer
2k
views
Is there any potential associated with magnetism?
Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is equal to $0$.
- 103