Question

In Walter Lewin's lecture while explaining the Leyden jar he says that the charge on the glass is 12 times more than that in the air gap.
How is this obtained ?

Basically there are 2 metal containers separated by a glass sheet. The air gap between the outer conductor and glass is 1 mm, the thickness of glass is 3 mm and the airgap between the glass and the inner conductor is 1 mm.
The electric fields in the air gap and glass are worked out to be as below :

(i)air gap of 1 mm thickness and electric field of 3*10^6 V/m in it
(ii)adjacent to air gap is : glass sheet of 3 mm thickness and electr

Answer 1

You start by saying: Eair=Ebreakdown=3 10⁶.
Then, as d_air=1mm, deltaV_air=3kV on each side.
So, you knew deltaV total=30kV, then deltaV_inner capacitor=24kV.

Now think of the inner capacitor as having 2 imaginary plates and a dielectric. You know deltaV=24kV, and E=sigma_inner/(kappa.eps0), and E.dist=deltaV, so you can solve for sigma.

Now forget about this inner capacitor, the outer capacitor has an E of 3 10⁶ V/m, which is equal to sigma_outter/eps0, so you can solve for sigma.

you then get that sigma_inner is about 13,3 times larger than sigma_outter.

Hope it helps.