Question

You have two flat metal plates, each of area $\mathbf{1}\mathbf{,}\mathbf{00}\mathbf{}{\mathbf{m}}^{\mathbf{2}}$, with which to construct a parallel-plate capacitor. (a) If the capacitance of the device is to be 1.00F what must be the separation between the plates? (b) Could this capacitor actually be constructed?

Short answer

1. The separation b.
2. Since the distance between the plates is less than the size of an atom, the capacitor cannot be constructed.

Step-by-step solution

Given data

The area of each flat metal plate is$\mathrm{A}=1.00{\mathrm{m}}^2$

The capacitance of the device is C = 1.00 F.

Determining the concept

Using Eq.25-9, find the separation between the plates. From this value, conclude whether this capacitor can actually be constructed or not.

Formulae are as follows:

$\mathbf{C}\mathbf{=}\frac{{\mathbf{A\epsilon }}_{\mathbf{0}}}{\mathbf{d}}$

Where C is capacitance, A is the area, and d is distance.

(a) Determining the separation between the plates

Therefore, the distance between the plates is,

$$\begin{gathered} \mathrm{d}=\frac{{\mathrm{A\epsilon }}_0}{\mathrm{C}} \\ =\frac{(1.00{\mathrm{m}}^2)\times (8.85\times {10}^{-12}\mathrm{F}/\mathrm{m})}{1.00\mathrm{F}} \\ =8.85\times {10}^{-12}\mathrm{m} \end{gathered}$$

Hence, the distance between the plates is$8.85\times {10}^{-12}\mathrm{m}$

(b) Determining if the capacitor can be constructed

From part (a),

It can be observed that d is much less than the size of an atom$\left(~{10}^{-10}\mathrm{m}\right)$.

Therefore, this capacitor cannot be constructed.