a If we were to calculate the electric field made by that ch

a) If we were to calculate the electric field made by that charge at the indicated distance, what would be the uncertainty in our calculation due only to the uncertainty in the size of q1?

b) What is the uncertainty in our field calculation due only to the uncertainty in the charge separation r?

c) What is the total uncertainty in our electric field calculation due to the uncertainty in the size of q1 and the uncertainty in the charge separation r?

Solution

a) Electric field due to charge = kq1 / r^2

magnnitude ofE = (9 x 10^9 x 1 x 10^-6 ) / (0.62^2) = 23413.11 N/C

R = X Y / Z

deltaR = R sqrt[ (deltaX / X)^2 + (deltaY/Y)^2 + deltaZ/Z^2 ]

uncertainity = 23413.11 (0.2 / 1) = 4683.62 N/C

b) uncertainity = 23413.11 sqrt[ (2/62)^2 + (2/62)^2] = 1068.10 N/C

c) uncertainity = 23413.11 sqrt[ (2/62)^2 + (2/62)^2 + (0.2/1)^2] = 4802.89 N/C