Question

You have been hired by a "storm chaser" as an assistant. This individual loves to find locations at which tornadoes and violent lightning storms are occurring. While there, he takes photographs and makes electromagnetic measurements. You are on a chase with him to a lightning storm in Florida. He explains to you that a cloud layer and the ground can be considered as the plates of a capacitor that stores charge, with the ground being charged negatively. The capacitor continuously leaks charge due to the free charges in the air between the plates. In thunderclouds, however, various processes result in charge distributions that eventually lead to lightning, a phenomenon that delivers negative charge to the ground. Therefore, the lightning recharges the capacitor. Ahead of you is a cloud layer that the storm chaser measures to be of area 2.00 km2 and height 10 km above the ground. He then uses a special apparatus called a field mill to measure that the electric field under the cloud is 4.00 â 10^6 N/C.

He asks you to do a quick calculation of the charge on the cloud-ground capacitor (in C), so you can know what to expect if there is a bolt of lightning.

Answer 1

The value is
`q =  70.8\ C`

Step-by-step explanation:

From the question we are told that

The area is
`A =  2.0 \ k m^2 = 2000000 \  m`

The height is
`h  =  10 \  km  =  10000 \  m`

The electric field is
`E =  4.0*10^(6) \  N/C`

Generally the electric field is mathematically represented as

`E =  (q)/(A *  \epsilon_o )`

Here
`\epsilon_o }` is the permitivity of free space with value

`\epsilon_o }   =  8.85 *10^(-12) \  N \ m^2 /C^2`

=>
`4.0*10^(6) =  (q)/(2000000 *    8.85 *10^(-12) )`

=>
`q =  70.8\ C`