In fair weather the electric field in the air at a particula

In fair weather, the electric field in the air at a particular location immediately above the Earth\'s surface is 111 N/C directed downward. (a) What is the surface charge density on the ground? Is it positive or negative? magnitude^-9.8145548_Your response is off by a multiple of ten. nC/m^2 sign negative (b) Imagine the surface charge density is uniform over the planet. What then is the charge of the whole surface of the Earth? -500 kC (c) What is the Earth\'s electric potential due to this charge? -703 Mv (d) What is the difference in potential between the head and the feet of a person 1.65 m tall? (Ignore any charges in the atmosphere.) 703 Your response differs from the correct answer by more than 100%. V (e) Imagine the Moon, with 27.3% of the radius of the Earth, had a charge 27.3% as large, with the same sign. Find the electric force the Earth would then exert on the Moon. Magnitude N Direction (f) Compare the answer to part (e) with the gravitational force the Earth exerts on the Moon. F_gravitational/F_electric =

Solution

(a) E=Q/(4*pi*epsilon*r^2)=(Q/4pi*r^2)*(1/epsilon)=surace density/epsilon

111=surace charge density/epsilon

surface charge density=9.83*10^(-10) C/m^2

(d) Potential=E*d=183.15 Volts

(e)force =K*Q*q/r^2

Q=500 kC

q=135.5 kC

r=(R+0.273R)=1.273R where R is radius of earth

force =9.2*10^6 N

direction=away from earth

(f) Fgravitational =GMm/r^2=4.42*10^(23) N

so Fgravitationa/Felectric=4.8*10^16