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Nyfinscyf
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Homework Statement
An electric dipole with -q at the clouds of height h, and +q beneath the surface with height -h.
Given q=200 C, and h=6000m
Electric discharge occurs with electric field of 3000 V/m near ground level, and 200 V/m above the clouds.
Find the ranges where discharges are likely.
Homework Equations
[itex]\vec{E}=\frac{kq}{r^{2}}\hat{r}[/itex]
[itex]k=\frac{1}{4\pi \epsilon_{0}}[/itex]
[itex]E=\left| \vec{E} \right|=\frac{k \left| q \right|}{r^{2}}[/itex]
The Attempt at a Solution
I found an expression for the electric field at some point a distance z away from the ground
[itex]E=E_1 + E_2 = 2kq\frac{z^2 + h^2}{(z^2 - h^2)^2}[/itex]
plugging in z=0 (to find electric field at ground level) you get:
[itex]E=2kq\frac{1}{h^2}≈100 000 V/m[/itex]
And the closer you move to the clouds the larger the electric field gets, so the first range of discharges is simply 0 < z < h.
Now the second ranges of likely discharges above the clouds can come from the same expression but I can't simplify it to find an actual distance.
I tried setting E=200 but I can't simplify it. plugging in large numbers approx 130 000 m as z gives an electric field less than 200 V/m.
I don't think I'm approaching this problem correctly. Can anyone help me out?