175 N/C pointing radially inward, calculate the total charge on the Earth and th

Question

175 N/C pointing radially inward, calculate the total charge on the Earth and the charge per unit area.
C
nC/m2

(b) At an altitude of 270 m above the Earth's surface, the field is only 145 N/C. Calculate the charge density of the air (assumed constant). [Hint: See the Conceptual Example within the chapter that discusses "Field Lines for a Thin Spherical Shell".]
C/m3

Explanation / Answer

1) we have following constants: R-radius of the earth 6,400km=6,400,000 m 2) According to Gauss law: E(r)=Q/e, where Q is total charge inside the sphere with radius r. for the earth :E(R)=Q/e --> Q=E(R)*e=175*8.85e-12=1.55e-9 C 3) we also know that the filed is oriented inwards, that means that the total charge is negative! So Q=-1.55e-9C 4) to calculate the charge per unit area you need to devide total charge by total are of aerth surface s=Q/A=Q/4pR2=-1.55e-9/(4p*6400000^2)=-3e-24 C/m2 PART B 1) total charge within sphere Q=E*e=145*8.85e-12=1.3e-9 C 2) we know that the filed strenght is lower than on the surface of the earth, that means that some positive charge exists in the air. we know that total is -1.3e-9 and we know that tptal charge on earth is -1.55e-9. That means that positive charge in the air is q=1.55e-9-1.3e-9=0.25e-9 C 3) Volume of the air: V=4/3*p*(R+270)^3-4/3*p*R^3=1.4e17 m^3 ?=q/V=0.25e-9/1.4e17=1.8e-27 C/m^3

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