Question

[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.

Answer 1

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