58 On a dry winter day you scuff your leathersoled shoes acr

58. On a dry winter day, you scuff your leather-soled shoes across a carpet and get a shock when you extend the tip of one finger toward a metal doorknob. In a dark room, you see a spark perhaps 5 mm long. Make order-of-magnitude estimates of (a) your electric potential and (b) the charge on your body before you touch the doorknob. Explain your reasoning.

Solution

A)

Electric field strength of air

E=3*10⁶V/m

Potential difference

V=Ed =(3*10⁶)(5*10^-3)

V=1.5*10⁴ Volts =10⁴V (approx)

b)

The area of your skin is perhaps 1.5 m²,so model your body as a sphere with this surface area.

=>4pi*r²=1.5

r=0.3455 m

We need that we are at potential found in part A

V=Kq/r

=>1.5*10⁴ = (9*10⁹)*q/0.3455

q=5.76*10^-7C =10^-6C (approx)