Recent content by TSny

  1. TSny

    I Derivation of Hamilton's Principle: Questions

    At which point of the paper do you believe the author takes ##\delta \int L \;dt = 0## for granted? The paper starts with d'Alembert's principle in the form of equation (1) of the paper. Equation (4) is used to make a substitution in (1) to derive the "extended Hamilton's principle", equation...
  2. TSny

    I Gauss' law seems to imply instantaneous electric field

    You're not missing anything. When I posted #9, I was apparently missing something - my brain :oldsmile: The magnetic field in my example is static, but the electric field varies with time as given in post #5. Of course, there is no instantaneous signaling going on between the charge and the...
  3. TSny

    Variable mass system : water sprayed into a moving container

    I get the same result. A nice approach is to use momentum conservation in an inertial frame moving with the stream of water. After finding v(t) in this frame, it's easy to transform back to the earth frame.
  4. TSny

    I Gauss' law seems to imply instantaneous electric field

    Yes. That's right. In my example, the electric and magnetic fields at any point are time independent. So, no signal propagation can occur.
  5. TSny

    I Gauss' law seems to imply instantaneous electric field

    The potential at the field point ##p## at time ##t## is given by the retarded-time expression ##\phi(r, t) = \large \frac{q(t-r/c)}{4\pi\epsilon_0 r}##. When evaluating ##\nabla \phi##, we need to take into account that the numerator and denominator of ##\large \frac{q(t-r/c)}{4\pi\epsilon_0...
  6. TSny

    Please tell me where I am going wrong in this integral

    In the second line, the first integral has an integrand that is odd in ##y##. You cannot replace ##\int_{-\infty}^{\infty}## by ##2\int_{0}^{\infty} ##.
  7. TSny

    B Applying the Gauss (1835) formula for force between 2 parallel DC currents

    Equation (6) in the link reads $$\ddot r = \frac{\mathbf{r}\cdot \mathbf{\ddot{r}}}{r} - \frac{(\mathbf{r \cdot \dot{r}})^2}{r^3} + \frac{\mathbf{r \cdot \dot{r}}}{r} = \frac{\mathbf{r}\cdot \mathbf{a}}{r} - \frac{(\mathbf{r \cdot \dot{r}})^2}{r^3} + \frac{\mathbf{r \cdot \dot{r}}}{r}$$ When...
  8. TSny

    I Maxwell stress tensor

    The last term on the right is wrong. This term should represent the divergence of just the part of ##E_{ij}## given by ##-\frac 1 2 \delta_{ij}E^2##.
  9. TSny

    Motion in 2 dimensions

    Very nice explanation! I think it gets to the heart of the matter. By choosing the tangential force appropriately as a function of time, we can switch back and forth between oscillatory motion and uniform circular motion while maintaining constant acceleration magnitude. This problem reminds...
  10. TSny

    Motion in 2 dimensions

    Yes, I agree. And the arc length comes out nice.
  11. TSny

    Electric field due to arc shaped thin rod

    I don't understand why you say that "dEx is Rcosθ distance away". Both dE and dEx are associated with the same point, namely the origin: In what sense is dEx located a distance Rcosθ away?
  12. TSny

    Electric field due to arc shaped thin rod

    Your answer is wrong because you can't get the x-component dEx by replacing R in the denominator of dE by Rcosθ. Note that Rcosθ < R when θ≠0. So, kdQ/(Rcosθ)2 is greater than kdQ/R2 when θ≠0. That is, your expression for dEx is greater than the expression for dE. But the component of a...
  13. TSny

    Electric field due to arc shaped thin rod

    No. Let's forget dEx for now. Just concentrate on dE. dE is the magnitude of the electric field vector dE at the origin O produced by the charge dQ in the diagram in post #2. In the general formula dE = kdQ/r2, what would you use for the distance r in this case?
  14. TSny

    Electric field due to arc shaped thin rod

    What was your reason for writing the denominator of the integrand as ##(R\cos \theta)^2##? This is not correct. To find ##E_x## due to the entire charge ##Q##, you need to understand that ##E_x = \int dE_x## where ##dE_x## is the x-component of the field vector ##\overrightarrow{dE}## due to an...
Back
Top