Question

After you walk over a carpet on a dry day, your hand comes too close to a metal doorknob and 3.0 mm spark results. Such a spark means that there must have been a potential difference of near to 6 kV between you and the doorknob. Assuming this potential difference, how much charge did you accumulate in walking over the carpet? For this extremely rough calculation, assume that your body can be represented by a uniformly charged conducting sphere 25.0 cm in radius and electrically isolated from its surroundings

Answer 1

1.69 * 10^(-7) C

Step-by-step explanation:

We can find this by using the formula for electric potential while making charge the subject of formula:

V = kQ/r

=> Q = (V*r)/k

Where k = Coulumbs constant

V = electric potential

Q = charge

r = distance between doorknob and charged body

From the question,

V = 6 kV = 6000 V

r = (25 + 0.3) cm = 25.3 cm = 253m

Note: Since we assume that the body is a sphere and we know that the charge in a sphere is concentrated in it's center, we add the radius of the sphere to the length of the spark (which tells us the distance between the doorknob and body) to get the distance between the doorknob and the charge.

Hence:

Q = (6000 * 0.253)/(9 * 10^9)

Q = 1.69 * 10^(-7) C