4
votes
Will the photon ever reach the object falling into the black hole?
Ivella asked: "How do you calculate if the object will ever receive the light signal before reaching the center of the BH?"
The photon doesn't always reach the falling object. In the ...
- 10.5k
4
votes
What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
Your second equation with its $({\bf E}\cdot {\bf E})\nabla$ isnot really correct as the nabla has to act on one of the ${\bf E}$'s. The correct form is best written as $({\bf E} \cdot \nabla {\bf E})...
- 50.6k
3
votes
Accepted
Why the charge is zero in this problem?
You shoud get zero because you assume $\lambda(z)=\lambda_{0} z$ and therefore
$\lambda(z) < 0$ when $z <0$ and vice-versa. Since your integral is symmetic w.r.t. $z$ so the final result becomes ...
- 1,130
2
votes
Maxwell stress tensor for electromagnetic wave
four years later you might not be that interested in the answer, but better late than never.
The way you write your waves is right and convenient, so I'll work with that notation.
$$\vec{E} = (E_1\...
2
votes
Accepted
Help with Pulley Problem
The rope supporting $m_2$ is doubled up. Consider pulling $m_1$ all the way to the left as far as it will go, for rope length $L$. Now let $m_2$ fall as far as it can - since the rope is doubled up on ...
- 8,902
1
vote
Where does Energy get lost in the Rocket Ship propulsion vs "direct acceleration" scenario?
The missing energy goes into increasing the KE of the exhaust.
Note that at high rocket speeds there is actually “extra” energy rather than missing energy. This comes from decreasing the KE of the ...
- 92.1k
1
vote
Problem Based on Twin Paradox using Special Relativity
At the bottomline the question is related with the hyperbolic geometry of the 4-dimensional Minkowski space. But we go there step by step.
In the whole post the speed of light $c=1$.
Actually, in ...
- 8,628
1
vote
How to use the orbital speed equation for more than one satellite orbitting a planet?
This is a very badly worded and very unclear question.
Two satellites named α and β both of mass m are orbiting around a large mass M in circular orbits having radius R1 and 2R1 respectively. ...
- 44.4k
1
vote
Magnetic field in the left focus of an ellipse current loop
Referring to another post in Math SE, we have
\begin{align}
\mathbf B (-c,0,0) &= \frac{\mu_0 I}{4\pi} \oint_C \frac
{d\boldsymbol s \times (-c\, \mathbf i-\mathbf r)}
{|-c\, \mathbf i-\...
- 1,350
1
vote
Accepted
Work done by adiabatic expansion derivation
Some of my guesses are to substitute $\frac{PV}{R} = nT$, but no idea
where the $n$ disappears to. Any help is appreciated!
The equation
$$W=-C_{v}(T_{2}-T_{1})\tag{1}$$
Assumes one mole of an ideal ...
- 67.6k
1
vote
Accepted
How do we solve polar coordinates related questions?
Hint.
$\vec{F} \times (\vec{r}\times \vec{p})=\vec{r}(\vec{F}\cdot\vec{p})-\vec{p}(\vec{F}\cdot \vec{r})$ by BAC-CAB rule, aka the vector triple product.
- 2,472
1
vote
How do we solve polar coordinates related questions?
You will find that hard to solve because the cross product is not well defined in spherical coordinates.
That means any cross product you come across in spherical coordinates you will want to convert ...
- 7,142
1
vote
Help with Pulley Problem
I thought acceleration and distance remains the same in a pulley system because the string is always the same length.
The string is always the same length, but the amount of string between $m_1$ and $...
- 44.4k
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