14
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What counts as the Earth's mass? At which point would it increase or decrease?
A great tool for answering these types of conceptual questions is an order of magnitude estimate, or a Fermi estimate.
Let's assume the Curiosity Rover has about the same mass as a car. A quick ...
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5
votes
Understanding Gauss' Law with Spherical Symmetry
$\vec E = E\,\hat r$ and $\vec a = da \,\hat r$ where $\hat r$ is the unit vector pointing out from the origin and is perpendicular to the area $d\vec a$.
You are evaluating $\displaystyle \oint_{\rm ...
- 98.9k
3
votes
Accepted
What would be the net flux through any plane in between two charges of a dipole?
According to Gauss's law the outward flux through any surface surrounding total charge $q$ is $\frac q{\epsilon_0}$. Apply this to the positive charge in your dipole (that's with the negative charge ...
- 36.3k
3
votes
Accepted
Does the force of gravity equation include only one dimension?
The force acts in all three dimensions, the magnitude is 1 d. but $\vec{F}=-G\frac{Mm}{||r||^3}\vec{r}$ and $\vec{r}$ is 3d
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3
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What counts as the Earth's mass? At which point would it increase or decrease?
The real answer is "if you have to ask what counts as Earth-mass, it's a poor unit for the question at hand." We only use this for approximations, giving a sense of scale to otherwise ...
- 50.8k
2
votes
Accepted
Coulomb atraction inside a charged sphere
You are right that without the negative charge inside, the positive charge on the outer conducting shell will distribute evenly and that there will be no electric field inside the shell.
If we kept ...
- 58.3k
2
votes
Does the force of gravity equation include only one dimension?
Gravitational force, like all forces, is a vector comprising a direction in 3 dimensions and a magnitude. In some cases, the direction can be ignored, usually because in such a case the direction ...
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2
votes
Why does gravity obey an inverse square law?
the author explains why a three-dimensional universe implies an inverse square law.
This explanation is an appeal to your intuition, but it does not explain "why" the electric (or ...
- 22.5k
1
vote
Understanding Gauss' Law with Spherical Symmetry
To add to Farcher's answer, here's an outline of how you would prove that $\vec E=E(r)\hat r$.
In general, a continuous symmetry (translation, rotation) allows you to get rid of a coordinate ...
1
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What counts as the Earth's mass? At which point would it increase or decrease?
In addition to the previous answer: the mass of the Earth is not constant. You have examples of objects leaving the Earth, but the mass can also increase when meteorites (big or small) hit the Earth. ...
- 46.9k
1
vote
Why does gravity obey an inverse square law?
The argument is wrong. There are other fundamental forces (v.g. weak or strong force) that do not go like $1/r^2$, even if the 3d argument should apply to these just as they apply to gravity and the ...
- 46.9k
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