[Draw the electric field around Earth. Draw a Gaussian surface and use Gauss’ law, explaining your steps.]
If the Earth were a large conducting sphere, what would the (negative) surface charge density have to be to maintain an electric field of 150.0 N/C at the surface? Use ε0 = 8.85 x 10-12 C2/N m2 and give your answer to 2 s.f.
let Q is the total charge on the earth surface.
we know, earth radius, Re = 6.37*10^6 m
let Q is the total charge on the surface of the earth.
Imagine a gaussian spehre with radius Re.
charge elconsed by the gaussian sphere, Qin = Q
now using Gauss' law, integral E.ds = Q/epsilon
-E*A = Q/epsilon
-E*4*pi*Re^2 = Q/epsilon
Q = -E*4*pi*Re^2*epsilon
= -150*4*pi*(6.37*10^6)^2*8.854*10^-12
= -6.77*10^5 C
surface charge density = Q/A
= Q/(4*pi*Re^2)
= -6.77*10^5/(4*pi*(6.37*10^6)^2)
= -1.3*10^-9 C/m^2 <<<<<<--------Answer
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