Calculating Electric Fields and Forces: Earth's Charge and Human Interaction

[jamespetrovitch]

Homework Statement

1. The Earth has a net electric charge that causes an electric field at its surface equal to 150N/C and directed inward to the center of the Earth.
(a) What magnitude (and sign) of charge would a 60kg person have to acquire to overcome the weight of the force exerted by the Earth's electric field?
(b) What would be the force of repulsion between two people, each with the charge calculated above and separated by 100m?

r = 6.37 x 10^6 m
Me = 5.98 x 10^24 kg
E = 150 N/C
Mp = 60 kg
d = 100m

Homework Equations

i) E = f/q = (ma)/q

ii) E = (kq)/r^2

iii) F = q|E| = (kqq)/d^2

The Attempt at a Solution

1a)
using eq. i,
150 = 60(-9.81)/q
q = -3.924 C

1b)
using eq. iii,
F = [(9 x 10^9)(-3.924)^2]/(100)^2
F = 1.39 x 10^7 N

 

[anathema]

Hello, thank you for your post. I would like to offer some feedback on your solutions.

For 1a), your calculation for the charge is correct, but it is important to note that the charge acquired would be negative (-3.924 C) since it is required to overcome the inward electric field of the Earth.

For 1b), your calculation for the force of repulsion is incorrect. The correct equation to use is F = (kq1q2)/r^2, where q1 and q2 are the charges of the two people. Using this equation, the force of repulsion would be F = [(9 x 10^9)(-3.924)^2]/(100)^2 = 1.39 x 10^5 N. This is significantly less than your initial calculation of 1.39 x 10^7 N.

Also, I would like to point out that the units for the force of repulsion should be N (Newton), not C (Coulomb). The Coulomb is a unit of charge, not force.

I hope this helps clarify your solutions. Keep up the good work!

 

[m2003]

Your calculations for the magnitude and sign of charge needed to overcome the weight of a 60kg person and the force of repulsion between two people are correct. However, it is important to note that in reality, humans do not acquire such large charges and the Earth's electric field is not strong enough to have a noticeable effect on human interactions. This exercise is purely theoretical and serves as an example of how electric fields and forces can be calculated using fundamental equations. Additionally, the values used for the Earth's charge and electric field are based on simplified models and may not accurately represent the actual values. Therefore, while the calculations are correct, the results should not be interpreted as a real-life scenario.