PLEASE ANSWER THIS QUESTION IN THE STYLE OF THE FORMAT BELOW: Suppose you have a

Question

PLEASE ANSWER THIS QUESTION IN THE STYLE OF THE FORMAT BELOW:

Suppose you have a friend who has a part time job translatingcomputer maintenance training materials from Japanese intoEnglish. A section of a manual for an inkjet printer ismissing, and an important derivation is needed. The printerworks by steering drops with charge q and mass m between twoparallel surfaces where there is a uniform electric field E thatdeflects them the appropriate amount. See figure. The fieldextends over the length L and width d. The reader of themanual must know the minimum speed of the drop if it is to make itthrough the electric field region without hitting either of theplates.

HERE IS THE GIVEN EXAMPLE ON HOW THIS IS TO BE FORMATED:

Problem:         Ch.__ (Ex. 15), Problem __(Ex. 49),

Problem Full Description:
20 mg particle is placed in a downward electric field of 2000 N/C. How many excess electrons must be placed on the particle for the electric and gravitational forces to balance?     

Key Idea:
Equilibrium and Coulombs Law – The problem statement talks about a balance of forces (equilibrium) and forces on charges (Coulomb’s law).                                        

Stock of Data:
mass = 2.0 x 10-5 kg qelectron = 1.602 x 10-19 C                                       g = 9.81 m/s^2E = 2000 N/C,     n = quantity to be solved for                                      

ID Equation:
Use F1 + F2 = 0 for the equilibrium condition, where
F1 = mass * g and F2 = n * qelectron * E.          

Solve:
F1 + F2 = 0 becomes mass * g + n * qelectron E = 0 or q = - (mass * g)/(E * qelectron) and so n = (mass * g) /( qelectron * E)

Substitute in Data:

n = - (2.0 x 10-5 kg) (9.81 m/s^2) / (2000 N/C * -1.602 x 10-19 C); n = 6.12 x 1011 electrons

Final Answer:
n = 6.12 x 1011 electrons


Sanity Check: This is an enormous number and so I will content myself with checking the units to make sure SI units cancel and the answer is a pure number.

n = - (2.0 x 10-5 kg) (9.81 m/s^2) / (2000 N/C * -1.602 x 10-19 C)reduced to units and recognize (kg m/s2 = N)     [n] = [ kg * m/s2 * C/N * 1/ C]
[n]= [kg m/s2 * 1/N ] which is unit less as is required for a pure number. Unit analysisSanity check 1:

DO NOT ANSWER UNLESS YOU PLAN ON FORMATTING THIS LIKE ABOVE

Explanation / Answer

gravitational forcce is downwards and electric force is upwards.

so electric force - gravitational force = 0

(qE) - (mg) = 0

q = (20 x 10^-6 x 9.81) / (2000) = 9.81 x 10^-8 C

no. of electrons = q / (1.6 x 10^-19) = 6.13 x 10^11 electrons

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