It has been experimentally observed that the electric field in a large region of earth's atmosphere is directed vertically down wards. At an altitiude of $$300m$$, the electric field is $$60V/m$$ . At an altitude of $$200m$$, the field is $$100V/m$$. Calculate the net amount of charge contained in the cube of $$100m$$ edge, located between $$200m$$ and $$300m$$ altitude

Question

It has been experimentally observed that the electric field in a large region of earth's atmosphere is directed vertically down wards. At an altitiude of $$300m$$, the electric field is $$60V/m$$ . At an altitude of $$200m$$, the field is  $$100V/m$$. Calculate the net amount of charge contained in the cube of $$100m$$ edge, located between $$200m$$ and $$300m$$ altitude

Infinity Learn · Accepted Answer

φ$$E=$$∫$$bottomE1$$¯ds¯$$+$$∫$$topE2$$¯ds¯$$+4$$∫verticalE¯ds¯ φ$$E=$$∫$$bottomE1dscoso0+$$∫$$topE2dscos1800+4$$∫$$verticalEdscos900$$ φ$$E=E1$$−$$E2s$$ φ$$E=q$$∈$$0$$⇒$$q=$$φE∈$$0$$ $$q=E1$$−$$E2s$$∈$$0$$ $$=100$$−$$6010028.85$$×$$10$$−$$12$$ $$=3.54$$×$$10$$−$$6C$$

Gauss's law and its applications

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Gauss's law and its applications

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φE=∫bottomE1¯ds¯+∫topE2¯ds¯+4∫verticalE¯ds¯ φE=∫bottomE1dscoso0+∫topE2dscos1800+4∫verticalEdscos900 φE=E1−E2s φE=q∈0⇒q=φE∈0 q=E1−E2s∈0 =100−6010028.85×10−12 =3.54×10−6C

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