Question

An electron is released from rest at the negative plate of a parallel plate capacitor. The charge per unit area on each plate is = 2.2 × 10^-7 C/m^2, and the plates are separated by a distance of 1.3 × 10^-2 m. How fast is the electron moving just before it reaches the positive plate?

Answer 1

Answer:
`1.066* 10^7 m/s`

Step-by-step explanation:

Given

Charge per unit area on each plate(
`\sigma`)=
`2.2* 10^(-7)`

Plate separation(y)=0.013 m

and velocity is given by

`v^2-u^2=2ay`

where a=acceleration is given by

`a=(F)/(m)=(eE)/(m)`

e=charge on electron

E=electric field

m=mass of electron

`E=(\sigma )/(\epsilon _0)`

`a=(e\sigma )/(m\epsilon _0)`

substituting values

`v=sqrt{(2e\sigma y)/(m\epsilon _0)}`

`v=\sqrt{(2* 1.6* 10^(-19)* 2.2* 10^(-7)* 0.013)/(9.1* 10^(-31)* 8.85* 10^(-12))}`

`v=1.066* 10^7 m/s`