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^-3m

The electric field strength is (E) =1.20 ×10⁵N/C.

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

We know that E =V/d

Then voltage between the two disks is (V) =E*d =(1.20 ×10⁵N/C.)(0.50*10^-3m)=60Volts

From the relation Q =CV

Then capacitance is given by (C) =Q/V =ne/V =1.20 ×10⁹ *1.6*10^-19C/60=0.032*10^-10F =3.2*10^-12F =3.2pF

Now the area of the circular disc is given by

C =eoA/d

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

Now area of the circular disk (A) =pir² then r =Sqrt(1.80*10-4/3.14) =0.757*10^-2m

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