The diameter of the disks is 1.32 cm.
If n electrons each of charge e are transferred from one disc to another, calculate the total charge Q transferred from one disc to the other using the expression,
![Q=ne](https://tex.z-dn.net/?f=Q%3Dne)
Substitute 1.50×10⁹ for n and 1.6×10⁻¹⁹C for e.
![Q=ne\\ =(1.50*10^9)(1.6*10^-^1^9C)\\ =2.4*10^-^1^0C](https://tex.z-dn.net/?f=Q%3Dne%5C%5C%20%3D%281.50%2A10%5E9%29%281.6%2A10%5E-%5E1%5E9C%29%5C%5C%20%3D2.4%2A10%5E-%5E1%5E0C)
The potential difference V between the disks separated by a distance d is given by,
![V=Ed](https://tex.z-dn.net/?f=V%3DEd)
here, E is the electric field.
Substitute 2.00×10⁵N/C for E and 0.50×10⁻³m for d.
![V=Ed\\ =(2.00*10^5N/C)(0.50*10^-^3m)\\ =100V](https://tex.z-dn.net/?f=V%3DEd%5C%5C%20%3D%282.00%2A10%5E5N%2FC%29%280.50%2A10%5E-%5E3m%29%5C%5C%20%3D100V)
The capacitance C of the capacitor is given by,
![C=\frac{Q}{V} \\ =\frac{(2.4*10^-^1^0C)}{100V} \\ =2.4*10^-^1^2F](https://tex.z-dn.net/?f=C%3D%5Cfrac%7BQ%7D%7BV%7D%20%5C%5C%20%3D%5Cfrac%7B%282.4%2A10%5E-%5E1%5E0C%29%7D%7B100V%7D%20%5C%5C%20%3D2.4%2A10%5E-%5E1%5E2F)
The capacitance of a parallel plate capacitor is given by,
![C=\frac{\epsilon_0A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cepsilon_0A%7D%7Bd%7D)
Here, ε₀ is the permittivity of free space and A is the area of the disks.
Rewrite the expression for A.
![C=\frac{\epsilon_0A}{d}\\ A=\frac{Cd}{\epsilon_0} \\ =\frac{(2.4*10^-^1^2F)(0.50*10^-^3m)}{(8.85*10^-^1^2C^2/Nm^2)} \\ =1.36*10^-^4m^3](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cepsilon_0A%7D%7Bd%7D%5C%5C%20A%3D%5Cfrac%7BCd%7D%7B%5Cepsilon_0%7D%20%5C%5C%20%3D%5Cfrac%7B%282.4%2A10%5E-%5E1%5E2F%29%280.50%2A10%5E-%5E3m%29%7D%7B%288.85%2A10%5E-%5E1%5E2C%5E2%2FNm%5E2%29%7D%20%5C%5C%20%3D1.36%2A10%5E-%5E4m%5E3)
the area A of the disks is given by,
![A=\frac{\pi D^2}{4} \\ D=\sqrt{\frac{4A}{\pi } }](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%5Cpi%20D%5E2%7D%7B4%7D%20%5C%5C%20D%3D%5Csqrt%7B%5Cfrac%7B4A%7D%7B%5Cpi%20%7D%20%7D)
Here, D is the diameter of the disk.
![D=\sqrt{\frac{4A}{\pi } }\\ =\sqrt{\frac{4(1.36*10^-^4m^2)}{3.14} } \\ =0.01316m\\ =1.32cm](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%5Cfrac%7B4A%7D%7B%5Cpi%20%7D%20%7D%5C%5C%20%3D%5Csqrt%7B%5Cfrac%7B4%281.36%2A10%5E-%5E4m%5E2%29%7D%7B3.14%7D%20%7D%20%5C%5C%20%3D0.01316m%5C%5C%20%3D1.32cm)
The diameter of each disc is found to be 1.32 cm.