All Questions
11
questions
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
1
vote
0
answers
61
views
Why does the term $-\frac{q}{c}\frac{d\vec{A}}{dt}$ play no part in the Lagrangian of a charged particle in an electromagnetic field? [duplicate]
A common derivation of the Lagrangian of a charged particle in an electromagnetic field starts with the Lorentz force that is rewritten in terms of the electromagnetic potentials $\Phi(\vec{x})$ and $\...
- 353
0
votes
2
answers
660
views
Derivation of Lagrangian of electromagnetic field from Lorentz force
I was trying to derive Lagrangian for the electromagnetic field from Lorentz's force formula
$$\mathbf{F}= q(\mathbf{E} + \mathbf{v}\times \mathbf{B})$$
I have to find the potential by using the line ...
- 59
0
votes
3
answers
141
views
Different definitions of the EMF of a device - None of them applies to devices in a circuit
Wikipedia gives two formal definitions of the electromotive force:
One in case of a closed loop, in which case the the EMF is supposed to be the path integral of the electric field (and all other ...
- 6,773
0
votes
1
answer
61
views
Will a led, connected to a long conducting rod, shine when the rod is falling through the magnetic field of the Earth?
Visualize a long conducting rod of length $l$ falling towards the Earth (after being released from a hight of say $5(km)$) perpendicularly to the Earth's magnetic field.
Near the earth's equator, ...
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
-1
votes
1
answer
840
views
Motion of an electric charge within an electric field with two electric charges
Assume that air resistance and gravity are negligible and the only significant force acting in the scenario is the electric force.
There are two electric charges, both with an equal and positive ...
0
votes
1
answer
230
views
Deriving Konopinski's Operational Definitions of Scalar and Vector Potential
In "What the electromagnetic vector potential describes", E. J. Konopinski asserts:
Operational definitions of $\phi$, $\mathbf{A}$ should now be expected to stem from the equation of ...
- 1,357
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