## y2o2 2 years ago The magnitude of the electric field vector on the ground is 100 N/C and it's direction towards the ground and perpendicular to it . The magnitude decreases as we go further from the ground till it reaches 20N/C at height 1400m. Calculate the average volume charge density (ρ) of the air layer between the ground and this height.

1. Vincent-Lyon.Fr

Do you know Maxwell-Gauß equation: $$\vec\nabla.\vec E = \rho/\epsilon_o$$

2. y2o2

Actually No , I still haven't studied the all the Maxwell equations. I studied Gauss law , but I didn't study the divergence form of it. I don't know if it can be solved by Gauss law. ${\int\limits_{}^{} E.dA = } {Q \over \epsilon_o}$

3. Vincent-Lyon.Fr

Ok, now you have to choose a Gaussian surface that goes from the altitude O to 1400 m. Work out flux of E, then you will get Q. Divide by volume and you will get $$\rho$$.

4. y2o2

I thought of this , but I couldn't do it. because I don't know the right G.surface to choose , and also I wasn't given any area to find a volume

5. Vincent-Lyon.Fr

Use any cylinder of base A and height h = 1400 metres. Volume inside cylinder will be: V = A.h