Electromagnetism Problem, electric charge per unit volume.

[Spoony]

Homework Statement

The atmostspheric electric fields at heights of 100m and 1000m above the surface of the eartg are 110 v/m and 25 v/m respectively and are directed downwards. Evaluate the averge electric charge per unit volume in the atmostsphere between these heights. Express your result as the number of ions per unit volume assuming that each ion carries a charge of magnitude 1.6x10^-19

Homework Equations

Value of Epsilon nought

The Attempt at a Solution

I am a little clueless about this problem. I think i may need to calculate the volume of the hollowed sphere between the two values (ie the volume of the 1000m sphere minus the volume of the 100m sphere giving me the total volume inbetween). But this doesn't sound right to me. Then how do i calaculate the electric charge per unit vol. from the electric field strength? Help would be appreciated muchly, i think i only need a prod in the right direction. Thankyou

 

[Spoony]

No-one has no idea how to solve this problem? No idea at all?

 

[ogb p]

I would approach this problem by first defining the variables and equations needed to solve it. The electric field strength, E, is given in the problem as 110 V/m at 100m and 25 V/m at 1000m. We can use the equation E = F/q to relate the electric field to the force, F, and the charge, q. We know that the force due to gravity, Fg, is equal to the weight of the atmosphere above a given height. Therefore, we can set F = Fg and substitute in the equation for the weight of a column of air, ρgh, where ρ is the density of air, g is the acceleration due to gravity, and h is the height.

Next, we can use the equation for electric field due to a point charge, E = kq/r^2, where k is Coulomb's constant, q is the charge, and r is the distance from the charge. In this case, we can set r equal to the distance between the two heights, 900m. We also know the value of k, which is 9x10^9 Nm^2/C^2.

Now, we have two equations with two unknowns, Fg and q. We can solve for q by setting the two equations equal to each other and solving for q. This will give us the total charge in the atmosphere between the two heights.

To find the average charge per unit volume, we can divide the total charge by the volume between the two heights, which can be calculated using the volume of a spherical shell equation, 4/3π(r2^3 - r1^3), where r2 is the outer radius (1000m) and r1 is the inner radius (100m).

Finally, we can use the magnitude of the charge of an ion, 1.6x10^-19 C, to calculate the number of ions per unit volume.

In summary, the steps to solve this problem are:

1. Define variables and equations: E = F/q, F = ρgh, E = kq/r^2, V = 4/3π(r2^3 - r1^3), q = number of ions per unit volume.

2. Set up and solve equations: E1 = F1/q, E2 = F2/q, set E1 = E2 and solve for q.