All Questions
15
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
0
votes
1
answer
238
views
Potential energy of two point charges of opposite sign (exercise)
I'm trying to do this exercise, but I don't understand how the textbook does it:
I don't understand, how they get a positive $27V$ and a got a few more doubts:
First thing, you can only measure ...
- 299
0
votes
1
answer
174
views
Motion of an electron near a proton [closed]
Statement of the problem:
Consider an electron and a proton that are initially at rest separated $a$ meters. Do not take into account the movement of the proton, because its mass is much greater ...
- 163
0
votes
1
answer
49
views
Decreasing energy but at expanse of what
question : A hollow spherical shell with radius R has charge Q uniformly distributed
over it.
(i) show that the energy
stored in this system is $\dfrac{Q^2}{8\pi \epsilon_{0}R}.$
(ii) Now imagine ...
user182868
1
vote
0
answers
527
views
Particle in electromagnetic field Lagrangian
Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
- 141
2
votes
1
answer
270
views
Lagrangian of a massive particle in an electromagnetic field
I am trying to find the Lagrangian of a massive particle in an electromagnetic field using the Lorentz force: $$ \vec F = q ( \vec E + \vec v \times \vec B)$$ with $$\vec E = - \nabla \phi - \frac{\...
- 43
-1
votes
1
answer
106
views
Direction of infinite plate when calculating the potential difference [closed]
Given the setting,
What is the potential difference between point $Q, ( {q ~\rm cm} , {0~\rm cm} )$ and point $P, ( {p~\rm cm} , {0~\rm cm})$? Let $q = 17.2~\rm cm$ and $p = 2~\rm cm$.
When ...
- 111
-1
votes
1
answer
193
views
Potential and Kinetic equality with scalar and vector potentials
I have to prove that:
$$\frac{d}{dt}\left( T+q\phi \right)=\frac{\partial}{\partial t}\left[ q\left( \phi - \vec{v}\cdot\vec{A}\right)\right] $$
Where $T=\frac{1}{2}mv^2$ is the kinetic energy and ...
- 211
1
vote
1
answer
902
views
Derivation of potential energy for Bohr's atomic model
I am trying to derive the total energy of the electron in Bohr's stationary orbit but I am finding it hard to derive the potential energy, i.e. how the potential energy is derived from the equation $$...
- 13
0
votes
0
answers
117
views
From Lagrangian of Electromagnetic field to the Lorentz force? [duplicate]
The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force
$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$
and ...
- 1,757
2
votes
1
answer
315
views
How is it possible to define a potential energy of a magnetic dipole if $\bf{B}$ is not conservative?
The magnetic field $\mathbf{B}$ is not conservative (it is not even irrotational). Nevertheless, considering a small loop (of area $S$ ) with electric current $i$ (equivalent to a magnetic dipole) in ...
- 2,607
-1
votes
2
answers
491
views
How to compute work needed to build a configuration of charges
Suppose an alignment of four charges in the vertices of a square. The first pair on one diagonal has positive charge and the other negative charge, all charges are of the same absolute value. length ...
-1
votes
3
answers
4k
views
Confusion in the derivation of the potential of a magnetic shell
I am reading an old book on electromagnetism (THE MATHEMATICAL THEORY OF ELECTRICITY AND MAGNETISM) and I have some confusion in the following pages:
First let me clarify what a "magnetic shell" is:
...
- 772
0
votes
1
answer
17k
views
Potential energy of the dipole-dipole interaction for two parallel dipole moments
I am looking for an equation that gives me the potential energy of the interaction between two parallel dipoles.
- 1,870
3
votes
2
answers
3k
views
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