Questions tagged [potential-energy]
Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.
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Does work done in a capacitor in moving a charge or increasing potential difference always twice the potential energy stored?
On doing calculations like this:
Work done in moving a charge across a potential difference = $(CV)V$ = $CV^2$
Potential energy increased = $(1/2)CV^2$
From this work done is twice the potential ...
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Self-Energy of a Conducting Shell based on Surface Charge Distribution
If a charge $q$ is given to a shell of radius $r$ (conducting or non-conducting) it's self-energy is $kq^2/2r$, $k$ being Coulomb's constant.
But if the shell is conducting and the charge on the inner ...
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In which situation the potential energy of a system is equal to its Gibbs free energy?
The other day I was giving a presentation about Transition State Theory, and I was showing both pictures of some potential energy surfaces (PES) and some Gibbs Free energy vs. reaction coordinate ...
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If I have a simple pendulum performing oscillations, whose string is snapped when it is at an extreme position, what will happen?
If I have a simple pendulum performing oscillations, whose string is snapped when it is at an extreme position, will it immediately fall vertically downwards because of gravity or will it continue ...
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Chemical Potential: sign of external potential energy
In statistical mechanics the total chemical potential $\mu _{\text{Total}}=\mu _{\text{Internal}}+\mu_{\text{External}}$. In the examples I have done so far $\mu_{\text{External}}$ is the external (...
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Saddle point and transition state of a molecule
During a transition of a molecule from one state to another, it pass through a transition state. This transition state, mathematically speaking, is a saddle point. That means, the second derivative ...
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Potential energy with constraints moving body
I know that for conservative forces $\vec{F}=-\nabla{U}$. Let's consider the case of gravitational potential energy, I know that $U=mgy$. Just to check: $\vec{F}=-\nabla{U}=(0,-mg)$: perfect!
Now, let'...
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Doubt in understanding the potential energy of dipole in external electric field?
When a dipole is placed in external electric field it experiences a torque $$\vec \tau = \vec p \ \times \vec E $$
whose magnitude is
$$||\vec \tau|| = ||\vec p|| \cdot ||\vec E|| \cdot sin\theta$$
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When is minimum potential energy in simple harmonic motion not zero?
We know that in simple harmonic motion, potential energy is minimum at the mean position and it is zero since displacement is zero. So what are some cases in which minimum potential energy is not zero?...
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Why does the mass-energy equivalence apply to binding energy when it is derived purely through kinematic means?
I understand that by defining the four velocity, multiplying it by the rest mass and taking the entire thing's norm we get $E^2=m^2+p^2$, but how does this apply to binding energy, or in general ...
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How is potential energy incorporated into mass in special relativity? [duplicate]
I've seen it said before that we often ignore potential energy in relativity because it can be included in the mass term. It is commonly said that a hydrogen atom has less mass than the sum of its ...
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How does the stress-energy tensor account for potential energy in static systems?
I see that the definition of the stress-energy tensor refers to the flux of momentum across a surface but given the example of a collection of electrons confined to a box (volume in space), even with ...
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Interpretation of gravitational potential in 2+1D
From Gauss's law of gravity reduced to 2+1 dimensions, one can easily show that the gravitational force follows an inverse law, i.e.
$$
\mathbf{F}(\mathbf{r}) =- \frac{G m M}{|\mathbf{r}|}\hat{\mathbf{...
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Coulomb force from a variational principle
See the attached discussion from Zangwill's Modern Electrodynamics, and in particular footnote 9. The point of this question is to understand how to recover Coulomb’s force law from an assumed form ...
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Confusions on The Gravitational Energy of a Point P in a Cube
I have been working, quite tirelessly, to try and find an answer to a question that has been bothering me for some time now.
I have been working over some proofs, in the Newtonian Mechanics world, to ...
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