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

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

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bonexptip 5 years 2021-08-11T14:30:15+00:00 1 Answers 282 views 0

Answers ( )

  1. Philomena
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    2021-08-11T14:31:31+00:00
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    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

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