Finding the Optimal Ratio for Two Concentric Spheres in a Capacitor

[Xinthose]

Homework Statement

It's desired to build a capacitor which has two concentric spheres separated by a dielectric of high permittivity, low loss, and high dielectric strength. Calculate the ratio of sphere b's radius to sphere a's radius which produces the lowest electric field between the spheres.

Not sure how to start this one. Thank you for any help.

 

[CWatters]

Sure this must have come up here before. Perhaps not the best one but..

https://www.physicsforums.com/showthread.php?t=347535

 

[Xinthose]

I do know, from Wikipedia, that concerning concentric spheres, Cap = 4 (pi) ε / ( (1 /a) - (1/b) )

 

[Nicholasc1988]

So what I've done on this problem so far is
C=[4pi(epsilon nought)][(ab)/(b-a)]
and
V=(Q/[4pi(epsilon nought)])(b-a)/(ab)
and plug it in Q=CV
i just get Q=Q

Conceptually
from E=kq/r^2 as the radius goes up the E field goes down
so the ratio from B to a would approach infinity or
A should be much less then A?

 

[CWatters]

The electric field E = V/d where d is the distance between the plates.

 

[Xinthose]

Alright, but you eventually get E = Q / (4 * pi * ε * a * b) ; so how would you get a ratio from that from b to a ?

 

[Xinthose]

You failed me Physics Forums; here is the scanned answer from my professor's solution set given to us after the test; I hope that this will help someone else out there; Make of it what you will; his handwriting is kind of hard to read

http://i633.photobucket.com/albums/uu57/Xinthose/scan0002.jpg

http://i633.photobucket.com/albums/uu57/Xinthose/scan0003.jpg

or if you prefer to see it on the forum

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