Question

Air "breaks down" when the electric field strength reaches 3 × 106 N/C, causing a spark. A parallel-plate capacitor is made from two 3.0 cm × 3.0 cm electrodes.How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

Answer 1

Answer:

$1.5\times 10^{11}}$

Explanation:

We are given that

Electric field=$E=3\times 10^6 N/C$

Dimension of parallel plate capacitor=$3 cm\times 3 cm$

Area of parallel plate capacitor=$A=3\times 3=9 cm^2=9\times 10^{-4}m^2$

$1 cm^2=10^{-4} m^2$

We have to find the number of electrons must be transferred from one electrode to the other to create  a spark between the electrodes.

$E=\frac{Q}{\epsilon_0A}$

Where $\epsilon_0=8.85\times 10^{-12}C^2/Nm^2$

Substitute the values

$3\times 10^6=\frac{Q}{8.85\times 10^{-12}\times 9\times 10^{-4}}$

$Q=3\times 10^6\times 8.85\times 10^{-12}\times 9\times 10^{-4}}$

$Q=2.4\times 10^{-8} C$

We know that

$Q=ne=n\times 1.6\times 10^{-19}$

Where e=$1.6\times 10^{-19} C$

$n=\frac{Q}{e}=\frac{2.4\times 10^{-8}}{1.6\times 10^{-19}}=1.5\times 10^{11}}$