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

`1.5* 10^(11)}`

Step-by-step explanation:

We are given that

Electric field=
`E=3* 10^6 N/C`

Dimension of parallel plate capacitor=
`3 cm* 3 cm`

Area of parallel plate capacitor=
`A=3* 3=9 cm^2=9* 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=(Q)/(\epsilon_0A)`

Where
`\epsilon_0=8.85* 10^(-12)C^2/Nm^2`

Substitute the values

`3* 10^6=(Q)/(8.85* 10^(-12)* 9* 10^(-4))`

`Q=3* 10^6* 8.85* 10^(-12)* 9* 10^(-4)}`

`Q=2.4* 10^(-8) C`

We know that

`Q=ne=n* 1.6* 10^(-19)`

Where e=
`1.6* 10^(-19) C`

`n=(Q)/(e)=(2.4* 10^(-8))/(1.6* 10^(-19))=1.5* 10^(11)}`