Question

You are trying to experimentally determine the electric potential of a conducting sphere, which you know is given by V=kQ/r. You experimentally measured the charge to be Q=3.2042e−19 C and the radius to be r=0.08 m, and also find you have an uncertainty in both of those quantities equal to ΔQ=1.6021e−21 C and Δr=0.005 m respectively. What is the uncertainty in V due to the uncertainty in your measurement of the radius r?

Answer 1

Uncertainty ΔV = 22.601 x 10^-10

ΔV = 2.2601nv or 2.2601 x 10^9V

Step-by-step explanation:

from V = kQ/r

Uncertainty in V is given by δV = V square root [ (δQ/Q)^2 + (δr/r)^2]

ΔV = V square root [ (ΔQ/Q)^2 + (Δr/r)^2] .....................(2)

Given that ; Q = 3.2042e−19 C, r = 0.08 m, ΔQ = 1.6021e−21 C, Δr = 0.005 m

Plugging the values given into equation (2)

from ΔV =(kQ/r) square root [ (ΔQ/Q)^2 + (Δr/r)^2]

ΔV = 9 x 10^9 x 3.2042e−19 / 0.08 square root [ (1.6021e−21/ 3.2042e−19)^2 + ( 0.005/0.08)^2]

ΔV = 360.47 x 0.06269 x 10^-10

Uncertainty ΔV = 22.601 x 10^-10

ΔV = 2.2601nv or 2.2601 x 10^-9V