# Physics and Astronomy Labs/The Leyden jar and the Van de Graff generator

## Is this safe? No!

${\displaystyle C=\epsilon _{0}{\frac {\epsilon _{r}A}{d}}}$

A is area, d is separation,

${\displaystyle \epsilon _{0}=8.854\times 10^{-12}}$  in SI units

For glass, the dilectric constant is ${\displaystyle \epsilon _{r}\approx 10}$  in SI units (actually between 3.8 and 14.5 according to Google[1])

The stored energy is

${\displaystyle U={\frac {1}{2}}CV^{2}\approx 2.15\,Joules}$

where C is capacitance and V is voltage, estimated using the rule of thumb of 40kV/cm for air breakdown. In the above calculation, we took 80 kV, and a 3 millimeter gap.

The consensus is that it is 2.15 Joules. Student labs are not 100% reliable, but here are the numbers as they called them in:

click to view raw data from students
1. ${\displaystyle 2.7\times 10^{-5}\,J}$  changed to ${\displaystyle 2.14\,J}$  because they forgot to square the voltage.
2. ${\displaystyle .826\,J}$  changed to ${\displaystyle 3.2\,J}$  after doubling the 40kV to 80 kV. But also used 3 instead of .003 and kept area in inches.
3. ${\displaystyle 2.15\,J}$
4. ${\displaystyle 2.148\,J}$
5. ${\displaystyle 2.15\,J}$

### From the internet

It seems that 10 Joules is dangerous. For that reason I would never touch 2 Joules, especially if I wasn't sure that it was exactly 2 Joules! Here is what I read on two internet sites:

• "Warning: A capacitor or capacitor bank capable of discharging 25 J in less than 3 seconds, or 10 J in less than 0.5 seconds, can be lethal." [2]

"It is generally and widely accepted that two caps with the same energy are equally dangerous. However, I am wondering this: Considering we are dealing high voltage caps and human touch with a specific resistance say maybe 1k ohm, is a certain Joule energy always equally dangerous and electrocuting regardless of capacitance ?

Let me illustrate with what I believe is considered a dangerous in capacitors, 10Jouls discharge: There is for instance around 10 Joules in 330V, 200uF capacitor. That is around maximum instantaneous starting current of 0.33A lasting about 0.2 seconds thru a 1kohm human. There is also 10J in a 1000,000V, 20pF Cap where the maximum instantaneous starting current through 1kohm human is 1000A lasting about(1/50,000,000 of a second). the difference between the above two caps however is that in the former cap, the duration of the 0.33A discharge is much longer than the duration of the 1000A in the latter, because of the equal joule energy. So as you get the picture and can see despite equal total 10J energy of the two caps, the discharges of the 2 caps are different in both duration and amount of current flow. One discharge has medium(lethal) current flow for a relatively long duration(0.2 seconds) while the other has an extremely high current flow(1000A) for an extremely short period of time at the beginning (1/50,000,000 of a second). (I know any cap discharge-power is actually a curve but you get the general picture of the discharge) Are the both caps therefore equally dangerous/electrocuting to the same 1khohm hand just because of the 10J and regardless of how the exact discharge-duration and power looks like? I hope you can see what I am trying to show and understand. All I really want to know is at what level the caps are dangerous..

## lab

Warning: This is a dangerous lab. Only a trained instructor should touch the equipment. A leyden jar can hold a dangerous charge even after you attempt to discharge it by making a spark.

Today we did a thrilling lab that was safe only because we took steps to keep it safe. A Leyden jar connected to a Van der Graff generator dramatically demonstrates the distintion between high voltage at low current and low voltage at high current.

• A Van der Graff generator by itself generates a spark of over 120kV (kilovolts), as can be verified by estimating the spark length and using the rule-of-thumb rule of 60kV/inch for breakdown of air.
• Connecting the Leyden jar reduces the spark length to about an inch, presumably because it takes so long to charge the extra capacitor that leakage inhibits the maximum voltage. But what a spark it makes!

There are safety concerns that need to be balanced before this becomes a Wikiversity resource. As we sport this out, we will post a video and images showing the spark, taken by user:13hartc.

The first of these images was recently drawn by our resident illustrator c:user:MarsLoveslions