6
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Conservation of energy and Coulomb's law
The reason why a medium changes the effective value of $k$ is because the medium itself consist of charges. In more formal Maxwell equation formulations one actually distinguishes between the real ...
- 65k
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Phase cancellation in beams of light- edited
Photons do not cancel each other, yes that would be a violation of conservation of energy. Photons are only created by excited electrons in atoms and they are only and always destroyed by absorption ...
- 2,863
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Under what conditions will a circuit violate conservation of charge and/or conservation of energy?
Kirchoff’s current law (KCL) implements the conservation of charge in a circuit. Kirchoff’s voltage law (KVL) implements the conservation of energy in a circuit. See Boundless Physics, various online ...
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Extra energy by applying torque?
In both cases the collisions are inelastic (as the bullet stops inside the block), so some of the initial kinetic energy is converted to heat due to friction between the block and the bullet. The ...
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Phase cancellation in beams of light- edited
But since photons carry energy from one place to another, what happens to the energy when they "cancel each other out" in this way? Where did it go?
The energy goes somewhere else where the ...
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Hamiltonian under the transformation induced by its own flow
Consider a solution of the Hamilton equations $x=x(t)$ with $x(0)=x_0$. By direct inspection,using the very Hamilton equations
$$\frac{d}{dt} H(x(t)) = \sum_{k} \frac{\partial H}{\partial q^k} \frac{...
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Conservation of energy and Coulomb's law
Consider a system of two point charges separated by a distance $r$.
In your equation $k=\dfrac{1}{4\pi\epsilon_{\rm r}\epsilon_0}$.
Increasing $k$ means that $\epsilon_{\rm r}$ must decrease, and this ...
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Velocity required for pendulum to make a full swing
Extending the answer by ProfRob, in order for the bob to travel in a circle there must always be tension greater than or equal to zero. If the bob is initially stationary at the top of the swing and ...
- 10.1k
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Virial Theorem: Application to simplify a PDE
For a non-trivial finite energy solution of the EOM of a one-dimensional system you can show that there is a kind of virial law. You can derive this by observing that potential and kinetic energy ...
- 326
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An object moving close to $c$ falling into a black hole
With:
$$ \eta \equiv \frac{c - v} c = 10^{-1000} $$
I think we have more than the energy of the BH increasing.
Note that:
$$ \gamma = \frac 1 {\sqrt{1-(1-\eta)^2}} \approx
\frac 1{\sqrt{2 \eta}} \...
- 39.5k
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An object moving close to $c$ falling into a black hole
The object's energy will simply increase the mass of the black hole.
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Energy to produce particles in different frames
The "nuclear" approach, valid for low-energy decays, equates available energy to the rest mass difference: $E = (m(X) - m(Y) - m(Z))c^2$. The "particle" approach, crucial for ...
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An object moving close to $c$ falling into a black hole
You are correct, but not for the reason you think. The mass of an object is a Lorentz scalar and therefore frame independent, meaning it does not change for different observers at different speeds. ...
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Why is rotational kinetic energy not explicitly considered in the energy analysis of a simple pendulum?
The simple pendulum is idealized. The bob is treated as a point mass. Furthermore, the amplitude is kept small enough that $sin(\theta) \approx \theta$. The mass of the rod is ignored. Friction is ...
- 45.6k
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Particle sliding on a sphere
This is my slightly simplified solution. I would like to thank my good friend @Bml for assistance with the calculus involved. (He is a bit of a whizz.)
The gravitational force acting on the sliding ...
- 10.1k
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Conservation of energy and Coulomb's law
Your example:
The reason this matches with energy conservation (whether there are bigger $k$'s or not) is that changing the medium in between requires energy itself.
Consider the charges kept fixed at ...
- 1,088
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vote
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Inconsistent result when finding the minimum speed to reach the highest point of a circular road
The minimum of $v_A$ makes $v_B=0$
The problem is that a car can't reach B and have zero velocity. If it has some tangential velocity, then it can't get rid of it at B since the only forces on it ...
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Phase cancellation in beams of light- edited
As I see it, the solution of the classical wave equation determines the probability of photon absorption. Assuming monochromaticity, the energy density divided by the photon energy gives the average ...
- 26.6k
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vote
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Potential difference across objects revolving around earth
It is possible to exploit this. It has been done. See the Physics LibreTexts chapter on Motional Emf.
Just producing a potential difference in a moving conductor does not produce energy. It is a like ...
- 45.6k
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How to understand the work-energy theorem?
In this answer I will derive the work-energy theorem twice: Section 1 presents a derivation that straightaway adresses the case of an arbitrary acceleration profile. This approach requires integration....
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