Question

The earth has a vertical electric field at the surface,pointing down, that averages 102 N/C. This field is maintained by various atmosphericprocesses, including lightning.

What is the excess charge on the surface of the earth? inC

Answer 1

`q = -461532.5 \ C`

Step-by-step explanation:

From the question we are told that

The electric filed is
`E = 102 \ N/C`

Generally according to Gauss law

=>
`E A = (q)/(\epsilon_o )`

Given that the electric field is pointing downward , the equation become

`- E A = (q)/(\epsilon_o )`

Here
`q` is the excess charge on the surface of the earth

`A` is the surface area of the of the earth which is mathematically represented as

`A = 4\pi r^2`

Where r is the radius of the earth which has a value
`r = 6.3781*10^6 m`

substituting values

`A = 4 * 3.142 * (6.3781*10^6 \ m)^2`

`A =5.1128 *10^(14) \ m^2`

So

`q = -E * A * \epsilon _o`

Here
`\epsilon_o` s the permitivity of free space with value

`\epsilon_o = 8.85*10^(-12) \ m^(-3) \cdot kg^(-1)\cdot s^4 \cdot A^2`

substituting values

`q = -102 * 5.1128 *10^(14) * 8.85 *10^(-12)`

`q = -461532.5 \ C`