Question

Suppose that after walking across a carpeted floor you reach for a doorknob and just before you touch it a spark jumps 0.95cm from your finger to the knob. Find the minimum voltage needed between your finger and the doorknob to generate this spark. The minimum field that can produce a spark in air is 3.0x10^6 V/m. V = _______ V

Answer 1

To solve this problem we will consider the definition of Minimum Energy, as the change between the minimum voltage and its distance. Mathematically it can be written as

$E_{min} = \frac{V_{min}}{r}$

Rearranging to find the Voltage,

$V_{min} = E_{min} \times r$

Replacing,

$V_{min} = (3.0) \times (0.95*10^4)$

$V_{min} = 28500V$

Therefore the minimum voltage needed between your finger and the doorknob to generate this spark is 28.5kV