(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A cross-section of a cylindrical high voltage terminal (inner cylinder) of a van de Graaff generator, surrounded by an 'intershield' (middle cylinder) and a pressure vessel (outer cylinder). The gas in the pressure vessel breaks down in electric fields greater than 1.6*10^{7}volts/m. If the radii of the terminal, intershield and pressure vessal are 1.5m, 2.5m, 4m respectively, what is the highest potential difference that can be maintained between the terminal and the pressure vessel? (hint: the intershield must be maintained at a potential such that breakdown is about to occur on its own outer surface as well on the surface of the terminal.)

2. Relevant equations

r_{terminal}=1.5m

r_{intershield}=2.5m

r_{pressure vessel}=4m

E_{max, p-vessel}= 1.6*10^{7}volts/m

∫E*ds= q/ε (Gauss's Law)

I believe E= q/ (2*pi*r*ε);where r= radius

V(r_{A}) - V(r_{B}) = -∫ q/ (2*pi*r*ε) dr ; V= potential energy, integrate from A to B

3. The attempt at a solution

E_{max,p-vessel}= q/ (2*pi*r*ε)

q=E_{max}*2*pi*ε*(4-2.5)

q=0.001335 C.

Would this q work for the entire cylinder if I changed the radius or is it just for the pressure vessel because that's where the electric field is?

Then,

V(r_{A}) - V(r_{B}) = -∫ q/ (2*pi*r*ε) dr

= -q/ (2*pi*ε)∫1/r dr

= -q/ (2*pi*ε)(ln(B)-ln)A) ; Where A,B would be the radius

plugging in q and using r_{i}=2.5m and r_{pv}=4m

= (-2.4*10^{7})*(-0.47)

= 1.128*10^{7}volts or 11.28 megavolts

I don't really know where to go from here, or even if this step is true. Is there any easier way I could be doing this?

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# Homework Help: Electric potential across a cross sectional cylinder

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