Ch23 Homework Solutions
23.**. 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 2.0 cm long. Air breaks down at a field strength of 3.0 x 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. Approximate your fingertip as a sphere of diameter 1.5 cm, and assume that there is an equal amount of charge on the doorknob 2.0 cm away.
(a) How much charge have you built up?
(b) How many electrons does this correspond to?Ooops. It is the diameter that is to be 1.5 cm, not the radius. I used Serway's assumption for your thumb but I did not include a charge on the doorknob. Since these are only approximations, I am going to leave this "as it is".
Q = 4.08 x 10 - 7 C
Q = 4.08 x 10 - 7 C [ 1 e / 1.6 x 10 - 19 C ]
Q = 2.55 x 1012 e
As we discussed in class, these are approximations and the E-field could break down the air any place along the 2 cm between your thumb and the door knob.
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