In fair weather, the electric field in the air at a particular location immediat
ID: 1427909 • Letter: I
Question
In fair weather, the electric field in the air at a particular location immediately above the Earth's surface is 132 N/C directed downward.
(a) What is the surface charge density on the ground? Is it positive or negative?
(b) Imagine the surface charge density is uniform over the planet. What then is the charge of the whole surface of the Earth?
3 kC
(c) What is the Earth's electric potential due to this charge?
4 MV
(d) What is the difference in potential between the head and the feet of a person 1.60 m tall? (Ignore any charges in the atmosphere.)
5 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.
(f) Compare the answer to part (e) with the gravitational force the Earth exerts on the Moon.
the signs are confusing me
magnitude 1 nC/m2 sign 2---Select---positivenegativeExplanation / Answer
Here,
electric field , E = 132 N/C
a) let the surface charge density is sigma
E = sigma/(2 * epsilon0)
132 = sigma/(2 * 8.854 *10^-12)
sigma = 2.337 *10^-9 C/m^2
the surface charge density is 2.337 *10^-9 C/m^2
as the electric field is downwards
the charge on the surface is negative
b)
total charge = sigma * 4pi * R^2
total charge = 2.337 *10^-9 * 4pi * (6.371 *10^6)^2
total charge = 1.192 *10^6 C
total charge = 1192 kC
the total charge on the whole surface is 1192 kC
c)
electric potential due to charge = k * Q/R
electric potential due to charge = 9 *10^9 * (1.192 *10^6)/(6.371 *10^6)
electric potential due to charge = 1.684 *10^9 V
d)
change in potential = electric field * distance
change in potential = 132 * 1.60
change in potential = 211.2 V
the change in potential is 211.2 V