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...
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!.
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}}##
You mean because centripetal acceleration "suddenly" appears there? As far as i know acceleration need not be continuous, its velocity that is usually continuous.
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...
@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.
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...
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.
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...
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.
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...
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...
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...
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.
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...
@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...
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...
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.
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...
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...
##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...
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...
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...
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?
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...
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.