Question

Two circular disks spaced 0.50 mm apart form a parallel-plate capacitor. Transferring 1.20 ×109 electrons from one disk to the other causes the electric field strength to be 1.20 ×105N/C.

What are the diameters of the disks?

**Express your answer with the appropriate
units.**

Answer #1

Given that

The distance between the two circular disks is (d) =0.50mm
=0.50*10^{-3}m

The electric field strength is (E) =1.20 ×10^{5}N/C.

The charge of an electron is (e) =1.6*10^{-19}C

We know that E =V/d

Then voltage between the two
disks is (V) =E*d =(1.20 ×10^{5}N/C.)(0.50*10^{-3}m)=60Volts

From the relation Q =CV

Then capacitance is given by (C) =Q/V =ne/V =1.20
×10^{9} *1.6*10^{-19}C/60=0.032*10^{-10}F
=3.2*10^{-12}F =3.2pF

Now the area of the circular disc is given by

C =eoA/d

Then A =C*d/eo
=(3.2*10^{-12}F)(0.50*10^{-3}m)/8.85*10-12
=0.180*10-3m2 =1.80*10^{-4}m^2

Now area of the circular disk (A) =pir^{2} then r
=Sqrt(1.80*10-4/3.14) =0.757*10^{-2}m

Then diamter of the disks is **(d) =2*r
=2*0.757*10 ^{-2}m =1.51*10^{-2}m=0.0151m or
1.51cm**

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