An electric field greater than about $3 \times 10^6 \textrm{ V/m}$ causes air to break down (electrons are removed from the atoms and then recombine, emitting light). See Section 17–2 and Table 17–3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Electric field is the voltage or the potential difference between two points divided by the distance between them. We can solve this for V by multiplying both sides by d. So V is electric field times distance. We have electric field of about 3 times 10 to the six volts per meter when air starts to have dielectric breakdown and starts conducting and you have a spark. That's times by the separation between your finger and the doorknob which is one millimeter, which is one times 10 to the minus three meters. So the voltage must be about 3,000 volts. There's no harm done because this is really the low current there is and not many electrons transferred between you and the doorknob. Voltage just says what is the tendency for charges to move. But it's actually the current that does harm to the body, which is the number of charges per second that move. And in this case, there is not very many charges, and so no harm done.