Question

Suppose the end of your finger is charged. Estimate the breakdown voltage in air for your finger. Assume The width of the end of a finger is about 1 cm. Express your answer to one significant figure and include the appropriate units. About what surface charge density would have to be on your finger at this voltage? Express your answer to one significant figure and include the appropriate units.

Answer 1

Solution:

a) Air starts conducting when the electric field exceeds 3 x 10^6 N/C.

Finger tip is assumed to be a part of a sphere of diameter 1 cm.,(region surrounding close to the sphere is assumed to be spherical)..

Break down Voltage = V = E * R = (3 x 10^6) ( 0.005) = 15000 Volts.

Since this is only an estimate it can be rounded to 20,000 volts = 2 x 10^4 V( 1 significant figure)

b) Surface charge density = Q/A = charge /area

Charge = (4 pi eo R) V since V = 1/ 4 pi eo * Q/R

So Surface charge density = $\sigma$ = ( 4 pi eo R) V / 4 pi R^2 = eo V/R = (8.85 x10^-12)(20000) / (0.005)

= 0.00000354 C/m^2

= 4 $\mu$ C/m^2 (one significant figure)