Question

The earth has a vertical electric field at the surface, pointing down, that averages 100 N/C. This field is maintained by various atmospheric processes, including lightning. If research came out on Planet x in a distant solar system that had a electric field with strength 222 N/C and 0.6 the radius of the earth, what would be the excess charge on planet x

Answer 1

q = 3.6 10⁵ C

Step-by-step explanation:

To solve this exercise, let's use one of the consequences of Gauss's law, that all the charge on a body can be considered at its center, therefore we calculate the electric field on the surface of a sphere with the radius of the Earth

r = 6 , 37 106 m

E = k q / r²

q = E r² / k

q =
`(100 \ (6.37 \ 10^6)^2)/(9 \ 10^9)`

q = 4.5 10⁵ C

Now let's calculate the charge on the planet with E = 222 N / c and radius

r = 0.6 r_ Earth

r = 0.6 6.37 10⁶ = 3.822 10⁶ m

E = k q / r²

q = E r² / k

q =
`(222 (3.822 \ 10^6)^2)/( 9 \ 10^9)`

q = 3.6 10⁵ C