As you are lying on the beach this past summer, you watch in awe as a super huge strato-nimbo-cummulus storm cloud roll in.
You pull out your iphone and use the "electroscope" App allowing you to measure the charge on the storm cloud. It reads +40C. You tell your bf/gf this and they say: "Wow that's a lot of protons!" You gently break the news about charge transfer and tell them exactly how many electrons have gathered on/left the cloud.
Meanwhile your friend has drawn a cloud in the sand. To impress (or annoy?) them, you add to their sketch the charge on the cloud AND the (induced) distribution of charge which accumulates on the earth directly below the cloud.
While watching the cloud, you see an aircraft is flying towards the cloud. This freaks your friend out b/c they are concerned for the safety of the plane and the people on it - it turns out his/her mother is on the plane! You estimate that the bottom of the cloud is at an altitude of 2000-m and the plane is at 1000-m. Furthermore, the plane is 2000-m east of the cloud.
Sketching this in the sand, and treating the earth and the cloud as point charges with equal but opposite charges (+40C for cloud and -40C for the earth) you find the electric field at the position of the plane. You add a sketch of the distribution of charges on the metal aircraft, but this just freaks your friend out even more. What would you say to reassure your friend if they are worried about the electric field inside the plane.
For this hand in please include the sand sketches and all the applicable calculations.
The Attempt at a Solution
To be honest I'm not even sure where to start.