To calculate the energy that the electron gives up as it passes between the electrodes of the spark plug, we can use the formula:
[tex]\[ E = q \cdot \Delta V \][/tex]
Where:
- [tex]\( E \)[/tex] is the energy in joules (J)
- [tex]\( q \)[/tex] is the charge of the electron (which is approximately [tex]\( 1.6 \times 10^{-19} \)[/tex] coulombs)
- [tex]\( \Delta V \)[/tex] is the potential difference between the cathode and anode (which is 10400 V in this case)
Let's substitute the values into the formula:
[tex]\[ E = (1.6 \times 10^{-19} \, \text{C}) \times (10400 \, \text{V}) \][/tex]
[tex]\[ E = 1.6 \times 10^{-19} \, \text{C} \times 10400 \, \text{V} \][/tex]
[tex]\[ E = 1.6 \times 10^{-19} \, \text{C} \times 10400 \, \text{J/C} \][/tex]
[tex]\[ E = 1.6 \times 10^{-19} \times 10^4 \, \text{J} \][/tex]
[tex]\[ E = 1.6 \times 10^{-15} \, \text{J} \][/tex]
Therefore, the energy that the electron gives up as it passes between the electrodes of the spark plug is [tex]\( 1.6 \times 10^{-15} \, \text{J} \)[/tex].
