Physics - Capacitor Question with Solution | TestHub

To find the distance $d$, we equate the capacitance of a parallel plate capacitor $C_{pp}=\frac{{ϵ}_{0}A}{d}$ to that of a metallic sphere $C_{sphere}=4\pi {ϵ}_{0}R$.

Given diameter $D=40$ mm, so radius $r=20$ mm $=0.02$ m. Area $A=\pi r^2=\pi (0.02{)}^2$ m${}^2$.

Sphere radius $R=1$ m.

$\frac{{ϵ}_0\pi (0.02{)}^2}{d}=4\pi {ϵ}_0(1)$

$d=\frac{(0.02{)}^2}{4}=\frac{0.0004}{4}=0.0001$ m $=0.1$ mm.

The final answer is $\boxed{0.1mm}$.