Answer:
2.63 mm
Explanation:
The capacitance of a parallel-plate capacitor is given by
[tex]C=\frac{\epsilon_0 A}{d}[/tex]
where
[tex]\epsilon_0[/tex] is the vacuum permettivity
A is the area of each plate of the capacitor
d is the separation between the two plates
In this problem, we know:
[tex]C=1.97 pF=1.97\cdot 10^{-12}F[/tex] is the capacitance
[tex]A=5.86 cm^2 = 5.86\cdot 10^{-4} m^2[/tex] is the area
Re-arranging the equation and substituting numbers, we can find the separation between the plates, d:
[tex]d=\frac{\epsilon_0 A}{C}=\frac{(8.85\cdot 10^{-12} F/m)(5.86\cdot 10^{-4} m^2)}{1.97\cdot 10^{-12}F}=2.63\cdot 10^{-3} m=2.63 mm[/tex]
