How Do You Calculate Average Volume Charge Density in a Layer of Air?

[kevinf]

In the air over a particular region at an altitude of 500 m above the ground, the electric field is 150 N/C directed downward. At 600 m above the ground, the electric field is 80 N/C downward. What is the average volume charge density in the layer of air between these two elevations?

the answer is supposed to be in C/m^3. i have looked at this question for a long time now and can not find a way to solve it. i think this problem would be easier if the volume of the slab of air of 100m height can be calculated and then use Gauss' law. but other then that i can not think of any other way to solve it. can anyone help me?

 

[LowlyPion]

In the air over a particular region at an altitude of 500 m above the ground, the electric field is 150 N/C directed downward. At 600 m above the ground, the electric field is 80 N/C downward. What is the average volume charge density in the layer of air between these two elevations?

the answer is supposed to be in C/m^3. i have looked at this question for a long time now and can not find a way to solve it. i think this problem would be easier if the volume of the slab of air of 100m height can be calculated and then use Gauss' law. but other then that i can not think of any other way to solve it. can anyone help me?

Well that is what you want to do isn't it?
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c2

Apply Gauss Law. Say you have a 100 x 1 cubic meter closed surface with field lines only going through 2 surfaces - top and bottom.

Isn't the net flux the charge inside, and the charge per cubic meter would be 100th of that?

 

[kevinf]

so should i just kind of make up a volume since it apparently isn't important?

 

[LowlyPion]

so should i just kind of make up a volume since it apparently isn't important?

It does make a difference.

The only information you are given are for the horizontal surfaces at 500m and 600m. You can ignore the vertical surfaces because the dot product of the E field and the vertical is 0.

You have 150/m² at the bottom and 80/m² at the top.