# Search results

1. ### Divergence of a radial field ##F=\hat{r}/r^{2+\varepsilon}##

Well you have compactified some steps (for example i would like to see the representation of the radial field in cartesian coordinates and the derivatives of ##r=\sqrt{\sum x_i^2}## with respect to each cartesian coordinate) but ok i am more than surprised that it can be done in less than half a...
2. ### Divergence of a radial field ##F=\hat{r}/r^{2+\varepsilon}##

Like the others i dont see anything wrong in your work. Maybe it is kind of simple because it is done in spherical coordinates. Try to do it in cartesian coordinates i think it would be one page long or even more!.
3. ### Problem about a triangle -- write the cos, sin and tan as a function of the sides

First use the pythagorean theorem to find the hypotenuse. Then use the definition of sin cos and tan on an angle of a right triangle. For example it is according to the definition that ##\sin\phi=\frac{a}{\text{hypotenuse}}##
4. ### Contradiction with forces in this problem with a ball rolling in a loop-the-loop ramp

You mean because centripetal acceleration "suddenly" appears there? As far as i know acceleration need not be continuous, its velocity that is usually continuous.
5. ### Calculate the New Velocity and the Velocity of a Pendulum Mass

Q2 is straightforward application of conservation of momentum. Q1 both a) and b) are about application of the principle of conservation of energy. I am sorry i am not allowed to say more according to the rules of PF you got to show us your best attempt at solution, which means you have to work...
6. ### What exactly is pulling the man up/down in rocket?

@PeroK post #4 might seem funny but he says a lot, its the force from the floor/seat that is responsible for this effect. Forget my post about fictitious forces.
7. ### What exactly is pulling the man up/down in rocket?

There are two answers in your question depending in which frame of reference we ll answer. In the accelerating frame of reference of the rocket, there is a fictitious force that presses the man down. Maybe its not the right time to be introduced to fictitious forces but you can google about...
8. ### Which direction should you aim to shoot a fish using a laser gun

Your book has its funny aspects, using high power laser to shoot poor fishes lol.
9. ### Proofs in analytic geometry and vector spaces.

There is indeed a problem with #2, you have to prove that it holds in any base but i dont understand the problem with #1, how are you supposed to work with vectors if you dont adapt a vector space(R^3 or R^2)? You are right that the proof with u and v is more general more complete i would say.
10. ### Why didn't ancient civilizations harness the power of electricity?

I think in ancient times, electricity and magnetism effects and phenomena though they were known, they were viewed as toy-like and ancient civilization just didnt put any research on these phenomena. They just couldn't imagine that one could make an electromagnetic engine e.g an electric motor...
11. ### I A real life problem with plumbing at my house

Its from the energy the water has due to its pressure (static pressure) which in turns comes from gravitational potential energy or from some pump that is located somewhere and increases the pressure of the water.
12. ### Distance Formula Problem

You shouldn't cross this in my opinion it was correct. It is just that it turns out that ##t_2=0## and ##d_2=1## which means that he has to run the second mile with infinite speed ##\frac{d_2}{t_2}=\infty##. But the problem asks if it is possible, so i guess the answer here is NO it isnt...
13. ### Vector potential ##\vec A## in terms of magnetic field ##\vec B##

I have to look it up abit more thoroughsly (give me time to think heh ) but we can agree for now that your equation is correct in the case of non time varying currents. It doesnt seem to be correct in the case of time varying currents cause then the well known expression for A contains the...
14. ### Vector potential ##\vec A## in terms of magnetic field ##\vec B##

Are you sure this is the equation derived by Feynman? This equation obviously fails if ##\mathbf{B}=constant\neq 0## cause it gives ##\nabla\times \mathbf{B}=0## and hence ##\mathbf{A}=0##. I have in mind a slightly different equation which i derive from Helmholtz decomposition theorem which is...
15. ### Remainder of polynomial

This formula you wrote $$f(x)=Q(x)(x-1)(x+1)+R(x)$$ says a lot if you know how to interpret it. Since (x-1) divides f(x) what can you say about whether (x-1) divides R(x)? I believe this and together with the answer to the question of @haruspex will get you to the answer of the question.
16. ### Other Questions about physics and math unsolved problems

If the problems are too hard, hard enough to be the subject of a PhD thesis, then I guess there is no generic process on solving them, other than Understanding very well the theory (know and understand all the theorems and definitions that are related) behind the problem Understanding what the...
17. ### Rigorous Study of the Higgs Boson - Question

@vanhees71 I have a specific question about the math required to learn QFT. Is tensor calculus absolutely necessary for someone that wants to learn QFT? Back at the era of my undergraduate studies (mid 90s) tensor calculus was not an obligatory source in my math department and i didnt take the...
18. ### Charged Conducting Sheet v. Charged Non-Conducting Sheet

Yes , the way i understand it is that when the distance of the electron is big, in comparison with the inter-electron spacing in the plate, then the force from the electron will be small in comparison with the interelectron forces in the plate, hence it wont affect much the positioning of...
19. ### Charged Conducting Sheet v. Charged Non-Conducting Sheet

Yes, but since the stopping point of the electron is just above the plate, there will be some fraction of the journey (when the electron gets very close to the plate) where the redistribution is not negligible, but yes this is a tiny fraction of the total journey of electron.
20. ### Charged Conducting Sheet v. Charged Non-Conducting Sheet

i am not so sure i understand you here, can you expand?
21. ### Charged Conducting Sheet v. Charged Non-Conducting Sheet

Strictly speaking you are right but for the level of this problem (i suspect high school or college level) we can safely consider as negligible the EM field produced by the moving electron (or just neglect the E-field in the quasi static approximation). Does it have analytical solution if we...
22. ### I Cases when Ampere's circuital law fails to hold

The symmetry is broken when the wire is of finite length. Due to broken symmetry, the magnetic field will not be the same along the closed amperian loop on which we perform integration, so ampere's law integral cant be simplified to ##B\cdot 2\pi r=\mu_0 I##. But it always hold that ##\oint...
23. ### B Is the length of the arm r in a polar coordinate a function of the angle?

##r## is to ##\theta## what ##x## is to ##y## in a cartesian coordinate system. They are independent coordinates. They can be related only if you try to describe a curve, for example the curve of a spiral ##r=a\theta## However the unit vectors ##\hat r,\hat\theta## depend on ##\theta## while in...
24. ### Homework about Motion on Plane

What exactly are the forces ##F_x,f_x,F_y,f_y##? I mean to what physical forces they do correspond? In my opinion there are only 2 forces acting on the block, gravity and the normal force, but they are immersed into 3D and not in 2D as we are used to for this kind of problems. So extra care is...
25. ### I Is there a difference between Faraday’s induction experiments?

So , something that is important for me personally, there are components of E and B such that the Poynting vector ##\mathbf{E}\times\mathbf{B}## is not zero but it falls faster than ##1/r^2## (it falls like ##1/r^4## for example for Lorentz boosted fields). I cant seem to be able to locate Eqs...
26. ### I Is there a difference between Faraday’s induction experiments?

So ##\frac{\partial \mathbf{B}}{\partial t}\neq 0## but is it ##\frac{\partial \mathbf{B}}{\partial t}=constant## that's why there is no radiation? What is a Lorentz-boosted field?
27. ### I Is there a difference between Faraday’s induction experiments?

In the frame where the magnet is moving, isn't the magnetic field time varying?
28. ### I Is there a difference between Faraday’s induction experiments?

Not sure, i think in this case the em wave will have a spectrum of frequencies and not a single frequency.
29. ### I Is there a difference between Faraday’s induction experiments?

Even in this case, I think an EM wave is being produced . That is because even when the magnet is moving with constant velocity, the magnetic field around the magnet is time varying, and according to Maxwell's equations a time varying magnetic field is always accompanied by a time varying...
30. ### I Is there a difference between Faraday’s induction experiments?

No, electromagnetic waves are being produced by the moving magnet as well. If the magnet oscillates mechanically back and forth with frequency ##f## then it is the source of electromagnetic waves of the same frequency ##f##. Generally any motion with acceleration of the magnet produces EM waves.