Exemplo 19.4 de College Physics, 19.2 Electric Potential in a Uniform Electric Field

What Is the Highest Voltage Possible between Two Plates?

Problema e solução em inglês, como no livro original.

Dry air will support a maximum electric field strength of about $3.0 \times 10^{6} V/m$ . Above that value, the field creates enough ionization in the air to make the air a conductor. This allows a discharge or spark that reduces the field. What, then, is the maximum voltage between two parallel conducting plates separated by 2.5 cm of dry air?

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Estratégia
We are given the maximum electric field $E$ between the plates and the distance $d$ between them. The equation $V_{AB} = Ed$ can thus be used to calculate the maximum voltage.
Solução
The potential difference or voltage between the plates is

$V_{AB} = Ed .$
19.28

Entering the given values for $E$ and $d$ gives
$V_{AB} = (3.0 \times 10^{6} V/m) (0.025 m) = 7.5 \times 10^{4} V$
19.29

or

$V_{AB} = 75 kV .$
19.30

(The answer is quoted to only two digits, since the maximum field strength is approximate.)
Discussão
One of the implications of this result is that it takes about 75 kV to make a spark jump across a 2.5 cm (1 in.) gap, or 150 kV for a 5 cm spark. This limits the voltages that can exist between conductors, perhaps on a power transmission line. A smaller voltage will cause a spark if there are points on the surface, since points create greater fields than smooth surfaces. Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through humid air. The largest voltages can be built up, say with static electricity, on dry days.

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