Case I: \"Mini-lightning\" Suppose that after walking across a carpeted floor yo

Question

Case I: "Mini-lightning"

Suppose that after walking across a carpeted floor you reach for a doorknob, and just before you touch it a spark jumps 6 mm between your finger and the knob.

a.) Find the minimum voltage difference between your finger and the doorknob for this to occur. __V

b.) Let's explore further-- first, calculate the capacitance of this system. You may approximate the doorknob and your finger as identical circular parallel plates, each of average radius 1.2 cm. Then calculate the charge that is on your finger to cause this spark.

C = __ pF
Q = __ nC

Explanation / Answer

The breakdown electric field is about 3 x 10^6 V/m (a) V = Ed = (3e6)(0.006) = 18,000 V (b) C = e0A/d A = pi*(0.012^2) d = 0.006 C = ((8.85e-12)(pi)(0.012^2))/(0.006) = 6.67 x 10^-13 F Q = CV = (6.67e-13)(18000) = 1.20 x 10^-8 C

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