All Questions
7
questions
0
votes
2
answers
132
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Gravitational potential and Bessel functions
In electromagnetism, we can solve Laplace and Poisson equation using Bessel functions. But my question is why don't we use Bessel functions to solve these equations for gravitational potential?
- 1
12
votes
1
answer
850
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Gravity vs. EM: action at a distance
Countless texts point to Newton's theory $\nabla^2\phi = 4\pi G\rho$, and remark that the problem here is that a distribution of mass determines the potential instantaneously everywhere, which is ...
- 366
1
vote
0
answers
302
views
Efficient calculation of potential energy of $n$-body system
Consider $n$ bodies which interact solely through Newtonian gravity/Coulomb force, then the total potential energy of the system can be obtained as:
$$U =\pm \sum_{1\leq i<j\leq n}\frac{G\alpha_i\...
- 413
5
votes
2
answers
1k
views
Why does field strength follow the inverse square law but potential does not?
Either in a gravitational or electrical field, let's say an electrical field, the electrical field strength follows the inverse square law. This is fairly intuitive just due to the geometry of the ...
- 109
1
vote
2
answers
195
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Electric voltage versus gravitational voltage across a unifom field
Let us say we have a uniform electric field, like between two charged plates separated by a distance $d$.
The formula for the voltage between the plates is $\Delta V=Ed$.
But what is the value of ...
- 527
0
votes
1
answer
1k
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How do multipole moments relate to a Taylor expansion, with regards to Newtonian potential?
Given the Newtonian gravitational potential,
$$ \phi(\mathbf{x}) = - \int \frac{G \rho(\mathbf{x'})}{|\mathbf{x} - \mathbf{x'}|}$$
One can construct a 'multipole expansion' by using the Taylor ...
- 1,751
2
votes
2
answers
753
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Modeling a potential well
I attempted to simulate the interaction of a moving particle and a potential well in Mathematica. The particle should experience a force of -$1/r^2$, if the equation for the potential well is -$1/r$. ...
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