Question

Suppose a Taser gun has its prongs have a distance of 9.5mm. Air
breaks down with a field strength of 30kV/cm. If an arc is formed at the
prongs of the Taser, determine the maximum voltage needed to create
this arc.

Answer 1

Under sufficiently strong fields, dielectrics become conductors, a situation called dielectric breakdown. The maximum voltage that a material can withstand without breakdown is called its dielectric strength E_m.

$E_m=\frac{V_{max}}{d} \to V_{max}=E_m \cdot d \\\implies V_{max}=(30 \frac{kV}{cm})(9.5\,mm(\frac{1\,cm}{10\,mm}))=28.5\,kV$

In conclusion, the maximum voltage needed to create the arc is 28.5 kV or 28500 V.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.