# Potential difference between Earth's surface and 2 meters above

Assuming Earth is a charged sphere of radius $R = 6400\times10^3$ m with uniform surface charge density $\sigma = -10^{-9}$ C/m2 and with $\epsilon_0 = 8.85\times10^{-12}$ F/m

I find that

$$V(R+2)-V(R) = \int_{R}^{R+2}E(r)dr = \frac{\sigma R^2}{\epsilon_0}(-\frac{1}{R+2} + \frac{1}{R}) = 226 V$$

If this is correct, why don't we feel that potential difference ?

• feynman wrote about it in Physics lectures, see here: peaceone.net/basic/Feynman/V2%20Ch09.pdf Answer seems to be that any conductor you bring into air will change that field. So there is no 300V between your head and feet. Mar 3, 2015 at 21:13
• May I ask where the value for the surface charge density comes from? Mar 4, 2015 at 0:05
• @Steeven it was given in the exercise, but it seems correct since Feynman mentions a similar potential difference (~200V).
– mwa1
Mar 4, 2015 at 9:04

## 1 Answer

Its because of the fact that we are touching the Earth, so we have the same potential as the Earth. Without a human in the vicinity of a "patch" on Earth, all we have are equipotential lines of 226V per meter by your estimation. When a human arrives at that place, because of the fact that the Earth tends to make us have the same potential with it(it can accept or give electrons in order to make the object that is touching to have the same potential), then the human will just readjust the equipotential lines, so as that the voltage difference between his legs and head is not big. This is explained in more detail(and much better than me) in the famous Feynman Lectures Vol.2

• When the electrons flow from the ground to our heads in order to bend the field lines, isn't that current ? Also, how are electrons going from the ground to our bodies if shoes are insulating ? Shouldn't we be at the same potential as the earth only if we're walking bare feet ?
– mwa1
Oct 31, 2015 at 14:32
• For the full discussion, check Feynman lectures Vol2 (can be found for free in the internet, just google it). Oct 31, 2015 at 14:51