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  1. Noctisdark

    Linear kinematics problem with limited variables.

    They will meat if ## x_1 = x_2 ## where ## x_1, x_2 ## are the equation of motion of rock 1 and rock 2, can you figure out what these equation are ?
  2. Noctisdark

    Analytical n

    Hello and welcome to the forum, Here in PF we are not allowed to directly answer any homework question .the help you get is proportional to your efforts ;) ! How do you think one can solve this problem ? How about a differential equation ?
  3. Noctisdark

    Different formulae for moment of inertia

    I just want to get a little deep into this and present what brainpushups said mathematically, any object can be represented at a set of points, each of these point have a moment of inertia ## \delta I = \delta m\cdot r^2 ## (this is true because they are points each of mass delta m), and we...
  4. Noctisdark

    Compare charge and current

    I agree with: As you've already said, current is defined as the amount of charge flow per second, there could be many charges little charges but summing them up will result in 1 C, bigger volume mean less resistance so more current flow this can be explained (the bad way) because charges have...
  5. Noctisdark

    Equation of motion from given 2D Potential

    You are doing it the wrong way, there are vector involved and ##\frac{d}{d \vec r} = \nabla ## and everyone already says it: force is the gradient of the potential, can you work it out now ? [Edit: In case I wasn't clear, ##\nabla = \lt \frac{\partial}{\partial x}, \frac{\partial}{\partial y}...
  6. Noctisdark

    Non-intuitive velocity change for object with changing mass

    ## m = e^{-t} ## means that after while the mass is basically zero, this is impossible a better suggestion will be ## m = m_0 + a*e^{-t}## where ##m_0## is the mass of the container and ##a## is the initial mass of the water, however as I've seen above momentum will not be conserved, but even...
  7. Noctisdark

    Electromagnetic nature of light

    This is a result of special relativity, magnetic field are electric field seen from a moving frame, this is mainly due to lorentz contraction, neutral field from our frame of reference may not be neutral in other frames, so they exert a force orthogonal to the motion (because contraction is...
  8. Noctisdark

    Probability of a distrubition

    I come to question about these things a lot and I totally agree with what you say and there is a way to find the most propable propability, even though we aren't aware of where stuff is and we don't know their state for sure, we don't know that no matter what they wouldn't (and shouldn't) smash...
  9. Noctisdark

    Is Quantum Mechanics an artifact of our ignorance?

    Quantum mechanics in real then, it's a very disturbing and enermously un-intuitive fact, but I somewhat enjoy it, the detective who is allways guessing where the particle is following its foot prints, but there's no freaking foot-prints !, there's only an empty road (potential) and you should...
  10. Noctisdark


    Since there is no initial velocity, ## x = \frac{at^2}{2} ##, you know what the acceleration is, the time is also given and ##\frac{1}{2} ## is ##\frac{1}{2}##, work it out !!
  11. Noctisdark

    Is Quantum Mechanics an artifact of our ignorance?

    Yes, I got that, but I have a simpler question that can make things more clear, if we were a virus of just very small, can we still observe these quntum phenomena?, that virus may even obey a quantum mechanical rule, how would it feel to jump from a place to another (when a scientist does the...
  12. Noctisdark

    Is Quantum Mechanics an artifact of our ignorance?

    I've read a lot about QM and studied the math and how it work many and many times in several lectures in several places, but whenever I review what the theory says and compare it to how the measurement work, I come to doubt in the theory it self, I think it can even be explained using classical...
  13. Noctisdark

    Tensors algebra

    Now since we know how we can represent a vector in a fairly simple co-ordinates, can we know it's magnitude, or it's dot product with other vectors ?, yes we can and for that purpose I shall introduce the great and wonderful (I allways liked it's name) the metric tensor, it written as ##g_{\mu...
  14. Noctisdark

    Tensors algebra

    First of all you must know why these are used, they are called dual co-ordinates, they are used because sometimes we need to change system of co-ordinates, as you may know in GR, co-ordinates are very wacky, they are nothing like cartesian(etc...) systems, so one has to come up with ideas to...
  15. Noctisdark

    Electric field due to a charged sphere

    ##\vec E = \frac{\sigma}{2\epsilon_0}\int \frac{sqrt{(R^2 - Z^2)(z-Z))}dZ}{(R^2 + z_0^2 -2Zz_0)^{\frac{3}{2}}} \hat z ##
  16. Noctisdark

    Electric field due to a charged sphere

    I think spherical coordinates are more adequate, but cylindrical are easier in this case, however we're going to integrate over the whole sphere then both R (radius of each ring) and z would change, I have set z = z0 - Z (Z is the one that will vary here) and, the equation of a sphere in...
  17. Noctisdark

    Electric field due to a charged sphere

    Yes is the same problem in griffith book with the scary ! near it, the field due to a charged ring is ##d\vec E = \frac{\lambda}{4\pi\epsilon_0}\displaystyle\int\frac{Rzd\theta}{(R^2 + z^2)^{\frac{3}{2}}}\hat z ## so, ## \vec E = \frac{\lambda Rz}{2\epsilon_0(R^2 + z^2)^{\frac{3}{2}}} \hat z ##...
  18. Noctisdark

    Electric field due to a charged sphere

    I know that gauss law is pretty straight forward, ##\vec E 4\pi r^2 = \frac{4\rho \pi r^3}{3} \hat r ## then solve for E,you have then ##\vec E =\frac{\rho r \hat r}{3}##, but Griffith ask to do it with integration and personally, I'd like to know how,can someone help it ?
  19. Noctisdark

    Electric field due to a charged sphere

    Another problem that yet I haven't managed to solve, finding the electric field due to a charged sphere of radius R using integration Homework Equations Continuous charged distribution $$|\vec E| = \frac{1}{4\pi\epsilon_0}\displaystyle \int\frac{\rho (r') dV}{r'^2}$$ The Attempt at a Solution...
  20. Noctisdark

    Electric Field due to two circular line charges

    I agree with blue_leaf, the net electric field is the sum of both electric field due to each of the charged ring, ie ##|\vec E| = \frac{1}{4\pi\epsilon_0}\int \frac{z\lambda dArc}{(R^2 + z^2)^{\frac{3}{2}}}## It's clear that ##dArc = Rd\theta## and you integrate from 0 to 2π, z in the height of...
  21. Noctisdark

    Work done by magnetic field

    ##dW = \vec F \cdot d\vec x, ## so ## \frac{dW}{dt} = \vec F \cdot \frac{d\vec x}{dt} + \frac{d\vec F}{dt}\cdot \vec x ## in case of magnetic fields ##\frac{dW}{dt} = \vec F \cdot \vec v + \vec x \cdot \frac{d\vec F}{dt} = 0 + \vec x \cdot q(\vec a \times \vec B + \vec v \times \frac{d\vec...
  22. Noctisdark

    Electric field due to a charged disk

    ##|\vec E| = \frac{\sigma}{2\epsilon_0}\cdot(1 - \frac{z}{\sqrt{r^2 + z^2}}) ## Waow thank you very for your assistance :)
  23. Noctisdark

    Electric field due to a charged disk

    ##\lambda = \sigma dR## ##\vec E= \frac{\sigma z}{2\pi\epsilon_0} \int_0^r \frac{RdR}{(R^2 + z^2)^{\frac{3}{2}}} = \frac{-1}{\sqrt{R^2 + z^2}}## evaluate from 0 to r and I get ##|\vec E| = \frac{\sigma z}{2\pi\epsilon_0}\cdot(\frac{1}{\sqrt{r^2 + z^2}} - \frac{1}{z})##
  24. Noctisdark

    Electric field due to a charged disk

    Aw, I've missed that too, In fact I intended to make ##r## the radius of the rings but I wrote ##R## and sticked with it, Okey I'm going to edit that two, I think I wrote a wrong ##\lambda##, it's dR not dr too
  25. Noctisdark

    Electric field due to a charged disk

    I think it should be ##dr##, because I've followed the approach that cuts the circle into little parts, from ##r \text{ to } r+dr##,
  26. Noctisdark

    Electric field due to a charged disk

    Aw there a z missing,
  27. Noctisdark

    Electric field due to a charged disk

    I I've missed that, thanks ! I will Edit that right away, I've included the expression of the cosine in ##\frac{1}{(R^2 + z^2)^{\frac{3}{2}}}##
  28. Noctisdark

    Electric field due to a charged disk

    Homework Statement I'm reading Griffith-Introduction to electrodynamics, In chapter 2 about electrostatics, I've encounter few problems that I've managed, to solve (luck !!), I'm asked to calculate the electric field due to a charged disk of radius R in a point P above the center (Pic)...
  29. Noctisdark

    Evaporation problem

    This is an introductory text, but I will worka lot of thing , Good luck !! [Yes, Evaporation rate will increase, molecules can easily flee ]