How much negative charge do I accumulate by touching the earth?

1. May 24, 2013

aaronsky12

The Earth carries a negative electric charge of roughly 500 thousand Coulombs (according to different sources I've seen). If I touch the Earth I should therefore pick up some of this electric charge (through conduction) and become negative charged. Assuming the earth can modeled as a conducting sphere with radius 6371 km and me as a conducting sphere with radius 1 m, around how much negative charge would I accumulate? The reason I ask is because I'm trying to prove to myself that grounding does indeed render a charged object neutral (i.e. transfers all the object's charge to the Earth). Using the well known equation for two connected conducting spheres with different radii (see Example 3-13 on page 115 in David Cheng's "Field and Wave Electromagnetics, 2nd Ed."), I calculate 0.0785 C, which is way too big and must be wrong. Any help in this matter would be appreciated. Thank you.

Here is my calculation:

V_sphere=k*Q1/r1 (potential of conducting sphere with radius r1 and and net charge Q1) V_earth=k*Q2/r2 (potential of conducting sphere with radius of the Earth, r2, and and net charge of the Earth, Q2)

where k is a constant. If the sphere touches the earth then their potentials (V_sphere and V_earth) must be equal, assuming that the charges on the spherical conductors may be considered as uniformly disturbed. Setting V_Sphere=V_earth, we get:

Q1/r1=Q2/r2

Setting Q1+Q2=Qtotal, yields:

Q1=Qtotal*r1/(r1+r2)

Substituting Qtotal=500,000C, r1=1 m,r2=6371000 m (radius of earth is 6371km) I get:

Q1=0.0785C.

I feel this number is way too large to be correct. If you take coupling into account (by modeling earth as PEC plate and using image theory), the charge that is accumulated only gets larger! What am I doing wrong here? There seems to be no way you accumulate -0.0785 C of charge by touching the earth.

Every textbook I read just says that the Earth is so big that it acts as an infinite sink/source for charge... without an explanation or calculation to prove this.

Thank you.

2. May 24, 2013

Staff: Mentor

We are all touching earth all the time, astronauts and airplanes as an exception (and airplanes are still in the air, and tend to land from time to time).

I think the formula for those two spheres assumes that the separation of the spheres is large compared to their diameter, this is not true for you.

You get an upper estimate with the assumption that the whole charge is distributed over 7 billion humans (plus much more trees, bushes, houses and some other animals).

I think a more reasonable approach would be the assumption that charge is proportional to the (vertical?) surface area.