Question

Ask Your Teacher In the air over a particular region at an altitude of 500 m above the ground, the electric field is 120 N/C directed downward. At 600 m above the ground, the electric field is 110 N/C downward. What is the average volume charge density in the layer of air between these two elevations?

Answer 1

`1.475* 10^(-13)\ C/m^3`

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

A = Area

h = Altitude = 600 m

Electric flux through the top would be

`-110A` (negative as the electric field is going into the volume)

At the bottom

`120A`

Total flux through the volume

`\phi=120-110\\\Rightarrow \phi=10A`

Electric flux is given by

`\phi=(q)/(\epsilon_0)\\\Rightarrow q=\phi\epsilon_0\\\Rightarrow q=10A\epsilon_0`

Charge per volume is given by

`\rho=(q)/(v)\\\Rightarrow \rho=(10A\epsilon_0)/(Ah)\\\Rightarrow \rho=dfrac{10\epsilon_0}{h}\\\Rightarrow \rho=(10* 8.85* 10^(-12))/(600)\\\Rightarrow \rho=1.475* 10^(-13)\ C/m^3`

The volume charge density is
`1.475* 10^(-13)\ C/m^3`