# Question #7a264

Feb 26, 2017

$0.0025 m$, rounded to three decimal places.

#### Explanation:

Size of penny is $0.75$ inches ($19.05$ mm) in diameter.

Capacitance $C$ of a parallel plate capacitor as shown in the figure below is given by the expression

$C = \frac{k {\epsilon}_{0} A}{d}$
where ${\epsilon}_{0} = 8.854 \times {10}^{-} 12 F \cdot {m}^{-} 1$ is permittivity of space and $k$ is relative permittivity of the dielectric material between the plates. $k = 1$ for free space, $k > 1$ for all media, $\approx 1$ for air.

Assuming that the pennies are kept in air, inserting given values we get
${10}^{-} 12 = \frac{8.854 \times {10}^{-} 12 \times \left[\pi {\left(\frac{19.05}{2 \times 1000}\right)}^{2}\right]}{d}$
$d = 8.854 \times \pi {\left(\frac{19.05}{2 \times 1000}\right)}^{2}$
$d = 0.0025 m$, rounded to three decimal places.