IP The Electric Field of the Earth The Earth produces an approximately uniform e
ID: 1593443 • Letter: I
Question
IP The Electric Field of the Earth The Earth produces an approximately uniform electric field at ground level. This electric field has a magnitude of 110 N/C and points radially inward, toward the center of the Earth.
Find the surface charge density (sign and magnitude) on the surface of the Earth.
Given that the radius of the Earth is 6.38×106m, find the total electric charge on the Earth.
If the Moon had the same amount of electric charge distributed uniformly over its surface, would its electric field at the surface be greater than, less than, or equal to 110 N/C?
Explanation / Answer
as the radius of earth is very large
we can assume that earth is a infinite sheet of charge near the surface
let the electric field surface density is sigma
electric field= sigma/(2*epsilon_0)
- 110 = sigma/(2 * 8.854 *10^-12)
sigma = - 1.95 *10^-9 C/m^2
the surface charge density on earth is - 1.95 *10^-9 C/m^2
total charge on earth = area * surface charge density
total charge on earth = -1.95 *10^-9 * 4 *pi * (6.38 *10^6)^2
total charge on earth = -9.975 *10^5 C
the total charge on earth is -9.975 *10^5 C
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as the area of moon is smaller than the area of earth
for same charge
area density of moon is larger than the area charge density of earth
hence , electric field at the surface of moon will be greater than 110 N/C
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