Question

In the air over a particular region at an altitude of 219 m above the ground, the electric field is 141 N/C directed downward. At 319 m above the ground, the electric field is 103 N/C downward. What is the average volume charge density in the layer of air between these two elevations? (include appropriate sign in the answer).

Answer 1

`q'=9.735* 10^(-13)\ C/m^3`

Step-by-step explanation:

Given that

219 m above the ground, the electric field is 141 N/C directed downward.

At 319 m above the ground, the electric field is 103 N/C downward.

If filed is going in to the region then it taken as negative and If filed is going out to the region then it taken as positive.

So net flux = 114 A - 103 A

Net flux= 11 A

Now from Gauss law

`Net\ flux=(q)/(\varepsilon )`

`\varepsilon =8.85* 10^(-12)`

`11\ A=(q)/(\varepsilon )`

q= 11 A ε

The average volume charge density(q') is the ratio of charge to the volume.

Volume = A .h

h= 319 - 219

h= 100 m

`q'= (11\ A\ \varepsilon )/( A\ h)`

`q'= (11\  \varepsilon )/(h)`

`q'= (11* 8.85* 10^(-12))/(100)\ C/m^3`

`q'=9.735* 10^(-13)\ C/m^3`

So the charge per volume is
`q'=9.735* 10^(-13)\ C/m^3`