All Questions
Tagged with potential-energy homework-and-exercises
35
questions
2
votes
1
answer
1k
views
Gravitational binding energy and integrated potential energy not the same?
Before looking up the formula for the gravitational binding energy of a uniform sphere, I simply figured that the general formula for binding energy of an arbitrarily-shaped mass distribution would be ...
- 10.5k
2
votes
1
answer
1k
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What is the energy of interaction between a point charge and an infinite cylinder?
I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject.
I know, that I can consider the cylinder as a wire with the same charge density (...
- 711
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 ...
- 2,617
1
vote
0
answers
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 $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
- 141
1
vote
2
answers
307
views
Deriving gravitational potential energy - why is $r_0 = \infty$?
I'm wondering about some assumptions I have to make in deriving the gravitational potential energy. This arises from the following exercise:
-
Since the net force acting on the satellite is ...
- 3,200
1
vote
1
answer
13k
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Problem in Proving the potential due to concentric shells between the shells
Imagine a spherical shell having charge Q. The Electric Field exists outside. I bring a test charge from infinity to the surface of the shell (I bring it radially to simplify the calculation and ...
- 2,797
1
vote
2
answers
2k
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Prove there is an equipotential sphere between two point charges
Given two point charges of opposite sign I need to prove that inside the electric field they create there is an equipotential sphere.
I'm very positive that this is more geometry than anything else ...
- 351
1
vote
2
answers
2k
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Deriving gravitational potential energy using vectors
Here is my attempt at derivation:
First you must find a vector function for the gravitational force.
By the inverse square law, the magnitude of gravitational force between two bodies of mass $m$ ...
- 1,585
1
vote
2
answers
265
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A little confusion in the derivation of potential energy of a shell
This is a paragraph and a figure from The Feynman Lectures, He's trying to prove the Shell theorem for gravity:
If we rearrange $dm=2\pi y \mu ds$ we obtain $\dfrac{dm}{2\pi yds}=\mu$. In this ...
- 3,093
1
vote
2
answers
3k
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Wave function for step potential
Given the step potential
$$V(x)=\begin{cases}
0~~~~~~~~\text{if }~~x \leq 0 \\
V_0~~~~~~\text{if }~~x > 0
\end{cases}$$
Consider the case where $E < V_0$. In this region $x \leq 0$ we have ...
user100411
1
vote
1
answer
1k
views
Force and energy relation: in case of time dependent force
The equivalent problems are also found in Marion problem 7-22, and other formal classical mechanics textbook. Here what i want to know why instructor solution and some websites gives this kinds of ...
- 3,622
1
vote
1
answer
2k
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Force derived from Yukawa potential
This is with regards to problem 3.19 from Goldstein's Classical Mechanics,
A particle moves in a force field described by the Yukowa potential $$ V(r) = -\frac{k}{r} e^{-\frac{r}{a}},
$$ where $k$ ...
- 1,031
1
vote
3
answers
2k
views
Difference in elongation in spring if it is stretched gradually and suddenly?
A spring is hanging vertically with a mass attached to it . Gradually lowered mass stretches the spring by $x$ m . If same body attached to the same spring is released suddenly, the maximum stretch in ...
- 135
1
vote
2
answers
3k
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Turning points of particle
A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential:
$$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$
Determine the turning ...
- 101
0
votes
1
answer
80
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Conventions for work and energy are not going correct in this situation [closed]
Let us consider 2 objects A and B.
The initial PE of the objects be U(A)=10J and U(B)=0J. Let F be the force exerted by A on B. Suppose W be the work done by force F. Due to this the PE of both the ...
- 356