On a dry winter day, if you scuff your feet across a carpet, you build up a charge and get a shock when you touch a metal doorknob. In a dark room you can actually see a spark about 2 cm long. Air breaks down at a field strength of 3.4 10⁶ N/C. Assume that just before the spark occurs, all the charge is in your finger, drawn there by induction due to the proximity of the doorknob. Model your fingertip as a sphere of diameter 1.35 cm, and assume that there is an equal amount of charge on the doorknob 2 cm away. How much charge have you built up? Answer in units of nC and round to one decimal place. Note 1 nC = 10⁻⁹ C.