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Transformation of the affine connection
- Thread starter ehrenfest
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- Connection Transformation
Hello everyone,
I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$
In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”:
$$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$
with $$r_{q}(t)=(0,0,z_{q}(t))$$
(I’m aware this isn’t...
Hi,
I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem.
Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$
Where ##b=1## with an orbit only in the equatorial plane.
We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$
Ultimately, I was tasked to find the initial...
Boundary conditions:
The derived Dirichlet and Neumann boundary conditions
In terms of the magnetic scalar potential:
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