Work done to construct Dielectric Sphere with Offset Hollow Cavity?

  • Thread starter Thread starter TwoAyoyoprogrammer
  • Start date Start date
  • Tags Tags
    Dielectric Sphere
TwoAyoyoprogrammer
Messages
1
Reaction score
0
Homework Statement
Find the work done to assemble positively charged particles from infinitely far way, to create a uniformly charged dielectric sphere with charge +Q and radius R. There is an offset hollow cavity with radius R/2, and electrically neutral (no charge).
Relevant Equations
Work = integral dWork
My thinking would be to do a work integral
Work = integral dWork
= integral delta V dq
= integral delta V 4(pi r^2) dr

The problem is, is this possible with a single integral?
Due to the offset cavity, the electric field E will not be constant at a given r.
 
Physics news on Phys.org
A picture is worth a thousand words... Would you sketch such a picture?
 
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...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top