The charge obtained during the Millikan Oil Drop experiment is given by the foll

Question

The charge obtained during the Millikan Oil Drop experiment is given by the following: q( V, y, t) . Where "q" is a function of only 3 things; "q" is largely dependent on voltage; "V" is the voltage applied to the field, "y" is the distance that the drop fell, and "t" is the time the oil drop took to fall (given as a constant).

Experimental average results were found using equations 1-4 from above:

q = 2.4E-19 C (coulombs)

V= 248 J/C

y= 4.62E-04 meters

t (constant) = 10 secs.

Use the Standard Combined Uncertainty equation to calculate the Uncertainty for the charge found from the Millikan oil drop experiment. You can derive the differential equation for the uncertainty of the charge by hand or by using MathCAD.

Explanation / Answer

for applied electric potential V
time taken to fall = t
distance fell = y
so, from dimensional analysis
dimensions for V = M L^2 T^-3 A^-1
dimensions of t = T
dimensions of y = L
so for q/m we can write
so A T -1 * M -1= [ M L^2 T-3 A-1]^a [T]^b [L]^c
comparing
a = -1
2a + c = 0
c = 2
-3a+ b = -1
b = -1 + 3a = -1 - 3 = -4

so q = m*y^2/V*t^4

so, considering dm = 0
dq/q = sqroot((2dy/y)^2 + (dV/V)^2 + (4dt/t)^2)

by pugging in values of q,y,V,T we can find m ( given)

and by putting in values of dy,dV,dt we can find dq ( Not given)

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