Static electricity - Quantity of charge induced.

[Girish198]

Hi all,
Let us say I have rubbed cat fur with nylon. Is there any relation for determining the amount of charge (in Coulombs) induced on either of the materials?
Thanks in advance.

 

[CWatters]

I suppose if you know the capacitance of the cat then Conservation of Energy sets an upper limit on the charge :-)

E = 0.5 Q²/C

PS: I can't help work out the efficiency with which your mechanical energy is converted to electrical energy in the cat.

 

[Girish198]

Dear CWatters,
First, Thank you for the reply. Please consider the following - I need the static discharge energy as the final result. I have the capacitance (C) of the body. I know the resistance (R) to ground. I need the rate of charge accumulation (Q/t) or the amount of charge accumulation (Q) on a body when it/he/she is moving at a velocity 'v' or any other condition. I am what can be called a naive in PHYSICS. Please let me know if anyone has come across some relation which connects the mechanical world to the amount of static charge deposited.
Thanks and best regards
Girish

 

[CWatters]

I doubt it's possible to calculate it. Too many real world unknown factors effect the efficiency with which charge is accumulated. The best I can offer is an upper limit from Conservation of Energy...

For example the work you do rubbing the two together can be calculated from

Work = force * distance.

The resulting energy stored in the capacitance of the body can't be greater than that due to conservation of energy. The problem is that some unknown percentage of the applied force applied will be lost overcoming friction (released as heat) rather than charging the capacitor.

So you have an equation like

Energy applied = Energy losses + Energy stored in the capacitor

Filling in what you know gives..

Force * distance = ?? + 0.5CV²

You could run an experiment and measure the applied force, the velocity and the resulting voltage on the capacitor. That would allow you to calculate the percentage lost to friction (and other effects).

If you prefer you could work with Power rather than Energy...

Power = ΔEnergy/Time

so you have

Force * Distance/time = ?? + Power into the capacitor

which gives

Force * Velocity = ?? + Power into the capacitor

but you still have the unknown power loss due to friction and other effects which I think can only be determined by experiment.

 

[Girish198]

@CWatters
Thank you. You have given me an idea from which I can derive my charge induced. Force of friction x distance x efficiency (about 2 percent, from Van de Graaf generator efficiency)= energy stored in capacitor (0.5 x C x V2);