Interactions between the atoms and molecules of the Earth\'s atmosphere can ioni

Question

Interactions between the atoms and molecules of the Earth's atmosphere can ionize some of the particles and create electric fields in certain regions. These electric fields can be measured by sensors aboard weather balloons and other devices. For this problem, let's assume the electric field in a certain region of the Earth's atmosphere is directed vertically downward. At an elevation of 300 m, the electric field is measured to have a strength of 50 N/C, and at an elevation of 200 m, the electric field has a strength of 500 N/C. Let's consider a cubic volume of space occupying the region of space where the electric field exists. Each edge of the cube has a length of 100 m, with one face of the cube lying in a horizontal plane at an elevation of 200 m, and the opposite face of the cube lying in a horizontal plane at an elevation of 300 m. What is the net electric charge contained in this cubic volume of space?

Explanation / Answer

By Gauss law,

Total electric flux = q/eo

since flux is downwards, flux through vertical faces will be zero, bottom face will be positive, top face negative

500×(100×100) - 50×(100×100) = q/eo

4.5×10^6 = q/eo

q= 4.5×10^6 × 8.85×10^-12 = 3.98 ×10^-5 C

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