# Gauss's Law Equation Question

## Homework Statement

Suppose that the electric field in the Earth's atmosphere is E = 1.50 x 10^2 N/C, pointing downward. Determine the electric charge in the Earth. (The radius of the Earth is 6371 km, and the Coulomb's constant, ke, is 8.99 x 10^9 N · m2/C2.)

E=kQr/a^3
Q = E(a^3)/kr

## The Attempt at a Solution

I have the equation to solve this (E = kQr/a^3) and have rearranged it to Q = E(a^3)/kr, but my problem is that I don't know what r (or a) is. The earth's radius would be a, right? Or would it be r? If it's r, then what's a, and vice-versa? Please help me figure r and a's values out.

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SammyS
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## Homework Statement

Suppose that the electric field in the Earth's atmosphere is E = 1.50 x 10^2 N/C, pointing downward. Determine the electric charge in the Earth. (The radius of the Earth is 6371 km, and the Coulomb's constant, ke, is 8.99 x 10^9 N · m2/C2.)

E=kQr/a^3
Q = E(a^3)/kr

## The Attempt at a Solution

I have the equation to solve this (E = kQr/a^3) and have rearranged it to Q = E(a^3)/kr, but my problem is that I don't know what r (or a) is. The earth's radius would be a, right? Or would it be r? If it's r, then what's a, and vice-versa? Please help me figure r and a's values out.
Judging by the title you chose for this thread, you should be using Gauss's Law to solve this.

Can you state Gauss's Law?

E=kQ/r^2. This is under the applications section of the chapter on Gauss's law, but directly after an example problem that says to find the magnitude of the electric field at a point inside the sphere, we use E=kQr/a^3. Is that different from finding the magnitude of the electric field due to a point charge in the center of the sphere?

haruspex
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E=kQ/r^2. This is under the applications section of the chapter on Gauss's law, but directly after an example problem that says to find the magnitude of the electric field at a point inside the sphere, we use E=kQr/a^3. Is that different from finding the magnitude of the electric field due to a point charge in the center of the sphere?
The question says nothing about fields inside charged spheres. It mentions the field in the atmosphere (just above ground level, presumably) and charge within the sphere of the Earth.

SammyS
Staff Emeritus