You are a geologist studying the electrical field on a given region. You find that the electric field is vertical and perpendicular to the surface and has a value of 81 N/C. (This field is maintained by various atmospheric processes including lightning Give your answer in Coulombs. Give your answer to two significant figures for full credit. What is the excess surface charge on one square kilometer on the geologic region you are studying?

charge Qint = 7.17 10⁻⁴ C

Explanation:

For this problem we must use Gauss's law

F = ∫ E. dA = Qint / εₙ

let's form a Gaussian surface that is parallel to the surface, for example, a Cube. As the field is vertical and perpendicular to the surface, the field lines and the area vector are parallel whereby the scalar product is reduced to an ordinary product.

Φ = E A = Qint / ε₀

A = 1 km² (1000 m / 1km) ² = 1 10⁶ m²

We can calculate the charge

Qint = E A ε₀

Qint = 81 1 10⁶ 8.85 10⁻¹²

Qint = 7.17 10⁻⁴ C