Recent content by Helmholtz

  1. H

    What shape would produce the greatest electric field?

    Thank you for the reference paper, I found that to be a great help. I believe I now understand what the answer is, as derived in the paper.
  2. H

    What shape would produce the greatest electric field?

    Suppose you are given an incompressible material with a constant charge density. What shape would create the largest electric field at a given point in space? These seems like a calculus of variation problem, but I am wondering if there might be any clever trick. $$\vec E = \frac{\rho}{4 \pi...
  3. H

    Internal Forces in System of Particles

    Thank you. I looked over the integral again and see exactly what you are saying and better understand all of that work. I think I now understand. Here is where I see the 1/2 coming into play: $$\sum_{i,j} \int_1^2 \vec F_{ji} \cdot d \vec s_i = -\frac{1}{2} \sum_{i,j} \int_1^2 \left( \vec...
  4. H

    Goldstein Mechanics example motion of one particle in polar coordinates

    That looks right to me. I should note that in LaTex you can write time derivatives using the \dot, e.g., $$\dot r.$$ For higher time derivatives just put as many 'd's as there are time derivatives, e.g., \dddot r is : $$\dddot r.$$
  5. H

    Goldstein Mechanics example motion of one particle in polar coordinates

    The second term is taking into account that the radius can vary in time. Use the chain rule. You can also see that your second term doesn't have the right units, and you need a second time derivative somewhere.
  6. H

    Internal Forces in System of Particles

    I am following along with Goldstien's Classical Mechanics Book and I am on page 11. The text is breaking down the total potential energy of a system into two parts: the external conservative forces and the internal conservative forces. My question pertains to the internal forces. Writing the...
  7. H

    Runge-Kutta 4th order method (RK4) for second order Diff Eq

    I have figured it out, thanks DrClaude.
  8. H

    Runge-Kutta 4th order method (RK4) for second order Diff Eq

    Homework Statement Hello, maybe this is due to my lack of understand of RK4, but I have an equation: x'' + b^2*x=0 (derivatives with respect to variable t) and I need to use RK4 to find the solution on an interval. I can readily find solutions analytically, but my understanding of RK4...
  9. H

    Effects of Dielectric on capacitors

    Does this make sense to you now then? I was trying to imagine a circuit in which they could still be in parallel after disconnecting, but it would only lead to a short circuit such as: ...... ...____________... ..|...|...|... ..V...|...__|___... ..|...|...|...|... ..|...|...C_1...C_2...
  10. H

    Effects of Dielectric on capacitors

    Even when you disconnect them from the battery? I was thinking of a circuit like this: ...... ...__________... ..|...|... ..V...__|___... ..|...|...|... ..|...C_1...C_2.. ..|...|_____|... ..|...|... ..|__________|... ...... And then when you disconnect the battery it's in series in the square.
  11. H

    Slip condition for a pulled cylinder

    Thanks for the response. I have done that, but I didn't like what I did and I was wonder if this was something someone could confirm. Two forces directed in the same direction, one on top of the wheel, the other on the bottom. Forces add as such: F_1+F_2=ma (F_1 is the tension, F_2 is the...
  12. H

    Effects of Dielectric on capacitors

    I misread the question. I think it might be helpful to find the total charge placed on both capacitors. Then we know that this is the charge in the circuit after the battery is also disconnected. Then with the fact that capacitors in series have the same charge as one another it would be...
  13. H

    Effects of Dielectric on capacitors

    The charge on the capacitors do not change when you insert a dielectric. So as the capacitance goes up, the voltage goes down proportionally. So V_2 = V_0/k and C_2 new = C_2 * k Q_1=C_1 * V Q_2 = C_2 * V E_1 = V/d E_2 = V/(k*d) I think these are right.
  14. H

    What is the Height of the Step Potential if 25% of a 9 eV Beam is Reflected?

    Homework Statement A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential? (A) 4 eV (B) 8 eV (C) 3 eV (D) 1 eV (E) 5 eV Homework Equations √(R) = [√(E)-√(E-U)]/[√(E)-√(E_U)] The Attempt...
  15. H

    Electric Flux Through a Face of a Cube

    Homework Statement A point charge +Q is placed at the center of a cube. What is the electric flux through a face of the cube? Homework Equations Flux = Q/ε The Attempt at a Solution The answer is Q/(4ε), but I thought it should be Q/(6ε) which isn't even an option. I'm I crazy? Since there...
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