PHYSICS - Electricity and Magnetism Question - HELP Appreciated :) In fair weath

Question

PHYSICS - Electricity and Magnetism Question - HELP Appreciated :)

In fair weather, the electric field in the air at a particular location immediately above the Earth's surface is 171 N/C directed downward. Take the radius of the Earth to be 6370 km.

(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?
______ kC

(c) What is the Earth's electric potential due to this charge?
________ MV

(d) What is the difference in potential between the head and the feet of a person 1.50 m tall? (Ignore any charges in the atmosphere.)
_________ V

Explanation / Answer

Here,

electric field , E = 171 N/C

a) E = k * Q/R^2

E = -k * sigma * 4pi * R^2/R^2

171 = -9 *10^9 * sigma * 4pi

sigma = -1.512 *10^-9 C/m^2

the surface charge density on the ground is 1.512 *10^-9 C/m^2

it is negative

b)

for the total charge

total charge on planet = -1.512 *10^-9 * 4pi * (6370 *10^3)^2

total charge on planet = -770975.4 C

total charge on planet = -771 kC

c)

Earth's electric potential due to this charge = -9 *10^9 * 771 *10^3/(6370 *10^3)

Earth's electric potential due to this charge = -1.089 *10^9 V

Earth's electric potential due to this charge = -1089 MV

d)

difference in potential = 171 * 1.5

difference in potential = 256.5 V

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