Question #7a264

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Question #7a264

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Answer 1 · 2017-02-26T09:42:14

$0.0025 m$ $0.0025m$ , rounded to three decimal places.

Explanation:

Size of penny is $0.75$ $0.75$ inches ( $19.05$ $19.05$ mm) in diameter.
![wikimedia.org/wikipedia/commons]( useruploads.socratic.org )
Capacitance $C$ $C$ of a parallel plate capacitor as shown in the figure below is given by the expression
enter image source here

$C = \frac{k ε_{0} A}{d}$ $C=(kepsilon_0A)/d$
where $ε_{0} = 8.854 \times 10^{- 12} F \cdot m^{- 1}$ $epsilon_0=8.854xx10^-12Fcdot m^-1$ is permittivity of space and $k$ $k$ is relative permittivity of the dielectric material between the plates. $k = 1$ $k=1$ for free space, $k > 1$ $k>1$ for all media, $\approx 1$ $~~ 1$ for air.

Assuming that the pennies are kept in air, inserting given values we get
$10^{- 12} = \frac{8.854 \times 10^{- 12} \times [π {(\frac{19.05}{2 \times 1000})}^{2}]}{d}$ $10^-12=(8.854xx10^-12xx[pi(19.05/(2xx1000))^2])/d$
$d = 8.854 \times π {(\frac{19.05}{2 \times 1000})}^{2}$ $d=8.854xxpi(19.05/(2xx1000))^2$
$d = 0.0025 m$ $d=0.0025m$ , rounded to three decimal places.

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Question #7a264

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