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## Homework Statement

In fair weather, over flat ground, there is a downward electric field of about 150 N/C. A) assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 150 N/C pointing radially inwards, calculate the total charge on the Earth's surface. B) at an altitude of of 250 m above the Earth's surface, the field is only 120 N/C. Calculate the charge density.

## Homework Equations

[tex]E=\frac{k\left|q\right|} {r^2}[/tex]

[tex]\rho=\frac{q} {V}[/tex]

## The Attempt at a Solution

I only need help with part b)

[tex]\left|q\right|=\frac{Er^2} {k}[/tex]

[tex]\left|q\right|=\frac{(120 N/C)[6.371(10)^6 m +250 m]^2} {8.99(10)^9 Nm/C^2}[/tex]

[tex]\left|q\right|=5.42(10)^5 C[/tex]

We then have,

[tex]\rho=\frac{5.42(10)^5 C} {(4/3)(\pi)[(6.371(10)^6 m +250 m)^3-(6.371(10)^6 m)^3]}[/tex]

[tex]\rho=4.25(10)^{-12} C/m^3[/tex]

However, the answer should be [tex]\rho=1(10)^{-12} C/m^3[/tex] according to the back of the book. Suggestions?