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

Answer:

$q = -461532.5 \ C$

Explanation:

From the question we are told that

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

Generally according to Gauss law

=>   $E A = \frac{q}{\epsilon_o }$

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

    $- E A = \frac{q}{\epsilon_o }$

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

     $q = -102 * 5.1128 *10^{14} * 8.85 *10^{-12}$

     $q = -461532.5 \ C$