In many applications, oppositely charged parallel plates are used to \"suspend\"

Question

In many applications, oppositely charged parallel plates are used to "suspend" charged particles. In this example, a dust grain with net charge +1.5 pC is suspended between the plates. The plates have charge density 1.011C/m, with the bottom plate positive. Mathematical Analysis2 a. What is the mass of the suspended dust grain? b. Other grains of dust would also be suspended by this device. For example, if a dust grain had twice the mass of the original grain and was also suspended, what would be the charge of this other grain? c. What is the charge-to-mass ratio (ha) of all of the suspended dust grains?

Explanation / Answer

a)

From Newton's second law

qE=mg

=>m=qE/g

since electric field is given by

E=sigma/eo=(1*10-6)/(8.8542*10-12)=1.13*105 N/C

therefore mass of grain is

m=(1.5*10-12)(1.13*105)/9.8

m=1.73*10-8 kg

b)

since mass is directly proportional to charge ,therfore

m2/m1=q2/q1

=>q2=q1*(2)=2q

q2=2*1.5=3 pC

c)

q/m =(1.5*10-12)/(1.73*10-8)=8.68*10-5 C/kg

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