# Charging an object by friction

1. Sep 2, 2011

### avjt

Hi All.

I'm trying to get a quantitative sense of how much charge we can put on an object by rubbing: the 'triboelectric effect'.

To put it specifically, suppose I have a sphere of diameter 1 cm, made of thermocol (polystyrene). How much charge, approximately, can I reasonably expect to put on it by rubbing it with, say, some fur?

I'm looking for just an 'order of magnitude' -- like, is 1 microcoulomb reasonable? How about 10 uC? Or 100 uC? Or will it be lower -- like 100 nC or 10 nC...?

Thanks for the help...

Avijit

2. Sep 3, 2011

### sambristol

Odd as it may seem but your answer is not about the material your sphere is made of but its 'self capacitance' and the breakdown voltage of the surrounding air.

Since you mention coulombs I will do this in SI units.

Your sphere will carry its charge largely on the surface like a conductor even though it is an insulator. The capacitance of a conducting sphere is given by

C = 4 * Pi * epsilon * R where Pi =3.14 etc, epsilon is the permittivity of
space = 8.854.. * 10^-12 Farads / metre and R is the radius of the sphere in metres.

In practice you can charge the sphere to the breakdown voltage of air by repeated rubbing (think of a Van De Graaf generator). The breakdown voltage of air is 30 Kvolt per inch of radius of the smallest curvature of the discharging electrode as a rule of thumb
so V=3* 10^4 * R / (2.54 * 10^-2) if the radius of your sphere is in metres.

Lastly the charge in coulombs Q on a capacitance C charged to a voltage V is given by

C= Q/V so Q=C * V

Putting this all together you get

Q= (4 * Pi * epsilon * 3 *10^4)* R^2/(2.54 ^-2)

Putting in the numbers we get Q = 1.1 * 10^-4 * R^2

so for your 1 cm sphere we get Q= 1.1 * 10^-6 Coulombs ie 1.1 micro Coulombs

Note that this is the maximum as any surface roughness will greatly decrease this (the bumps have smaller radius of curvature to R in the above equation is reduced so greatly decreasing the charge.

3. Sep 3, 2011

### avjt

Thanks sambristol. Interesting to know that the charge will be independent of the material the ball is made of.

Cheers,

Avijit

4. Sep 4, 2011

### vizal

the charge a material can store depends upon the capacitance of that material .... that is how charge it can store before it starts leaking it out (in simpler terms) . u can keep on charging that object until it starts leaking the charges ....
the capacitance is all that matters and it only depends on the size and the shape of your object ......hope it helps ... :)

vishal