36 votes

How is energy "stored in an electric field"?

This question is deeper than you might expect. Neither energy nor an electric field is exactly what you might expect. First, physics is a description of the behavior of the universe. It is not the ...
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  • 27.1k
20 votes

How is energy "stored in an electric field"?

The idea is that all energy, including kinetic energy and EM energy (such as that stored in the capacitor) is localized in space, i.e. given any region of space, one can assign net energy to it, and ...
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14 votes

How is energy "stored in an electric field"?

It's a model, created to capture what is seen in experiments. If we attribute the energy of an electromagnetic interaction to the fields, we get the right answer. We don't have an alternative that ...
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  • 4,156
12 votes
Accepted

How is energy "stored in an electric field"?

What "is" an electric field? One way to look at the world is to see it as a cellular automaton; something resembling Conway's game of life. Of course it's not so simple — the playing field ...
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6 votes

How is energy "stored in an electric field"?

Very incorrect and oversimplified but somehow intuitive: Nature tries to "equalize" many "things". For example temperature. Water in every place within a bucket will eventually be ...
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  • 161
6 votes

Relation Between Gravitational Potential and Acceleration due to gravity

$V \ne -g$. For one thing, the gravitational potential is a scalar while $\vec g$ is a vector field, so they can't be equal. They aren't equal in magnitude either: $$ V = -\frac{GM}{r}$$ $$ \vec g = -\...
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  • 7,634
5 votes

How is energy "stored in an electric field"?

The stress-energy tensor At every point in space there is a density: Build a sphere (or any shape) of gravity sensors and measure the net acceleration into the sphere (technically the surface integral ...
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4 votes

How is energy "stored in an electric field"?

If you look at our equations for energy, you will see that they typically settle into two major categories: Energy associated with intrinsic properties of a "thing" Energy associated with ...
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  • 42.8k
3 votes
Accepted

Does electron-proton interaction and electron-electron interaction in an atom gives rise to a microscopic potential energy?

It’s a little weird that your textbook discusses intermolecular and internucleon potential energies, but leaves out electron-nucleus interactions. At ordinary temperatures, the nuclear degrees of ...
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  • 71.7k
3 votes

Why is Newtonian gravity linear and independent on the presence of other bodies?

Linearity essentially means that the field does not interact with itself. To give a counter-example, it is interesting to look at a nonlinear theory of gravity, such as General Relativity (which has ...
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2 votes

Why electrostatic energy of a capacitor is not taken as negative?

Whenever you think about potential, do not think of it as a value at one place. Rather, think of it as the difference between the value at one place and the value at another. When we say "the ...
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2 votes

Why electrostatic energy of a capacitor is not taken as negative?

The potential energy is positive because we're considering it relative to a "base case" or reference condition where the positive and negative charges are right next to each other in the ...
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2 votes
Accepted

Doubt from Arnold; Mathematical methods of classical mechanics (page 20)

It's an important result with a large scope. Let $U$ be the potential with a minimum for $x=\xi$. Taylor expansion near $\xi$ is: $$U(x)\simeq U(\xi)+(x-\xi)U'(\xi)+\frac{1}{2}(x-\xi)^2U''(\xi)$$ ...
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  • 2,349
2 votes

A question about the potential energy of ordered marbles in free space

Now imagine a huge collection of randomly positioned small massive marbles in a volume of free space, making the entropy of the collection a maximum. If the configuration is precisely defined, we are ...
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2 votes
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Why doesn't $\omega = \sqrt{\frac{U''(x_0)}{m}}$ work for a simple pendulum?

You have to understand where the division by $m$ comes from. This is because you are assuming the kinetic energy to be $K(\dot x) = \frac{m}{2}\dot x^2$. In general, the relevant quantity is $K''(0)$ ...
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  • 1,687
2 votes

How is energy "stored in an electric field"?

If we transfer one small $dq$ charge from one capacitor plate to other, then we need to do some work. Repeat the process like this again and again; this leaves a net negative charge on the first plate ...
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2 votes

Can a (conservative) four-force be derived from a scalar potential?

Your calculation is consistent, a bit misleading. You should view it as a constraint on the possibilities of $\Phi$ since the force $f$ must be spacelike. This is the case here since $\Phi$ has only ...
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  • 1,687
2 votes

Why does a spring have potential energy compared to a rod?

In practice there is no such thing as a perfectly rigid rod. All rods compress to some extent, so they are like extremely stiff springs, but they are such stiff springs that you can ignore the ...
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  • 18.8k
1 vote
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Mass-energy equivalence and gravitational potential energy

An object doesn't increase mass when its energy increases. The rest mass is the rest mass. Even with kinetic energy. If an object is moving, its mass doesn't increase. You can associate a mass to the ...
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  • 414
1 vote

Mass-energy equivalence and gravitational potential energy

In the view of general relativity, gravity in reality does not have any form of well-defined potential that can be considered "energy" in the same sense as the components of the stress-...
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  • 779
1 vote
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Latent energy as a component of Internal energy

I think the book's authors would have better avoided introducing conceptual confusion by mixing microscopic and macroscopic concepts without a good reference to statistical mechanics. First of all, ...
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  • 23.6k
1 vote
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Energy of a Continuous Charge Distribution

You will soon see that the splitting of charge density and potential into 2 distinct elements, is the same as splitting E into 2 elements. $$\vec{E}_{total} = \vec{E}_{1} + \vec{E}_{2}$$ $$W = \frac{1}...
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  • 4,436
1 vote

Why we say that total energy should be zero at infinity in the derivation of escape velocity?

The gravitational force is $F=-\dfrac{GMm}{r^2}$ which goes to zero as $r\to\infty$. As $r$ increases, the gravitational force decreases and eventially, at infinity, dies off. Remember that the force ...
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  • 6,420
1 vote

Potential energy in Special Relativity

In special relativity, the equation of motion in Galilean coordinates are: $$\frac{\text{d}\boldsymbol{p}}{\text{d}t} - \boldsymbol{F} = \frac{\text{d}}{\text{d}t}\left(\frac{m\boldsymbol{v}}{\sqrt{1-...
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  • 589
1 vote

How we will choose reference point for more than two particle system to calculate potential energy as in the case of of equilateral triangle?

The point of the potential energy is that its difference gives you work and thus it is determined up to an additive constant. You can use any constant whatsoever, but for certain problems some choices ...
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  • 5,588
1 vote
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If an object just spontaneously appeared, would it have gravitational potential energy?

Yes. Gravitational potential does not require a change in position, it requires a hypothetical change in position. Wikipedia defines gravitational potential as the energy "that would be needed to ...
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