Answer:
[tex]d = 0.018 m[/tex]
Explanation:
Charge on the plates of the capacitor due to transfer of electrons is given as
[tex]Q = Ne[/tex]
here we know that
[tex]N = 2.1 \times 10^9[/tex]
so we have
[tex]Q = (2.1 \times 10^9)(1.6 \times 10^{-19})[/tex]
[tex]Q = 3.36 \times 10^{-10} C[/tex]
now we have electric field between the plates is given as
[tex]E = \frac{Q}{A\epsilon_0}[/tex]
here we have
[tex]1.5 \times 10^5 = \frac{3.36 \times 10^{-10}}{A(8.85 \times 10^{-12})}[/tex]
[tex]A = 2.53 \times 10^{-4} m^2[/tex]
now we have
[tex]A = \frac{\pi d^2}{4}[/tex]
[tex]2.53 \times 10^{-4} = \frac{\pi d^2}{4}[/tex]
[tex]d = 0.018 m[/tex]
