In a galaxy far away a scientist named Mullizirk measures the speed of ascending

Question

In a galaxy far away a scientist named Mullizirk measures the speed of ascending/descending oil droplets which she has charged with various numbers of electrons, before (v1) and after (v2) applying an electric field, E. Given the viscosity coefficient of her atmosphere, MU, the density of oil, p, and the acceleration due to gravity on her planet, g, she is able to determine the charges using the formula that she derived from Stoke's Law: The units of force on her planet are in mulldynes (M) and the units of charge are in zirkombs. (a) What are the units of E? (b) Mullizirk obtains the following charges oil four oil drops: What is the charge of an electron on Mullizirk?s planet? (c) How many coulombs are in a zirkomb?

Explanation / Answer

(a)

Since we know the relation between force, charge and field as : F = q*E

So, E = F/q

Thus, unit of E = unit of F / unit of q = mulldynes/zirkombs

(b)

Let's assume the charge on a single electron as e.

Since only integral numbers of electrons can be transferred, so the charges given must be an integral number of e.

Lets assume drops 1,2,3,4 contain n1,n2,n3,n4 number of electrons respectively

So, we have :

n1*e = 2.56*10-12 ---(1)

n2*e = 7.68*10-12 ---(2)

n3*e = 3.84*10-12 ---(3)

n4*e = 6.40*10-13 ---(4)

Dividing (2) by (1) , we get : n2 = 3*n1

Dividing (3) by (1), we get : n3 = 1.5*n1

Dividing (4) by (1), we get : n4 = 0.25*n1

Minimum possible value of n1 so that n2,n3,n4 all are integers is : n1 = 4

Thus, putting this value in (1), we get :

4*e = 2.56*10-12 zirkombs

So, charge on single electron = e = 0.64*10-12 zirkombs

(c)

We know, charge on one electron = 1.6*10-19 Coulombs

Thus, 0.64*10-12 zirkombs = 1.6*10-19 coulombs

Thus, we get :

1 zirkomb = 2.5*10-7 coulombs

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