The electric potential gradient of the atmosphere
On an ordinary day over flat desert country, or over the sea, as one goes upward from the surface of the ground the electric potential increases by about $100$ volts per meter. Thus there is a vertical electric field $\FLPE$ of $100$ volts/m in the air. The sign of the field corresponds to a negative charge on the earth’s surface. This means that outdoors the potential at the height of your nose is $200$ volts higher than the potential at your feet! You might ask: “Why don’t we just stick a pair of electrodes out in the air one meter apart and use the $100$ volts to power our electric lights?” Or you might wonder: “If there is really a potential difference of $200$ volts between my nose and my feet, why is it I don’t get a shock when I go out into the street?” We will answer the second question first. Your body is a relatively good conductor. If you are in contact with the ground, you and the ground will tend to make one equipotential surface. Ordinarily, the equipotentials are parallel to the surface, as shown in Fig. 9–1(a), but when you are there, the equipotentials are distorted, and the field looks somewhat as shown in Fig. 9–1(b). So you still have very nearly zero potential difference between your head and your feet. There are charges that come from the earth to your head, changing the field. Some of them may be discharged by ions collected from the air, but the current of these is very small because air is a poor conductor. How can we measure such a field if the field is changed by putting something there? There are several ways. One way is to place an insulated conductor at some distance above the ground and leave it there until it is at the same potential as the air. If we leave it long enough, the very small conductivity in the air will let the charges leak off (or onto) the conductor until it comes to the potential at its level.  Then we can bring it back to the ground, and measure the shift of its potential as we do so. A faster way is to let the conductor be a bucket of water with a small leak. As the water drops out, it carries away any excess charges and the bucket will approach the same potential as the air. (The charges, as you know, reside on the surface, and as the drops come off “pieces of surface” break off.) We can measure the potential of the bucket with an electrometer. There is another way to directly measure the potential gradient. Since there is an electric field, there is a surface charge on the earth ($\sigma=\epsO E$). If we place a flat metal plate at the earth’s surface and ground it, negative charges appear on it (Fig. 9–2a). If this plate is now covered by another grounded conducting cover $B$, the charges will appear on the cover, and there will be no charges on the original plate $A$. If we measure the charge that flows from plate $A$ to the ground (by, say, a galvanometer in the grounding wire) as we cover it, we can find the surface charge density that was there, and therefore also find the electric field. Having suggested how we can measure the electric field in the atmosphere, we now continue our description of it. Measurements show, first of all, that the field continues to exist, but gets weaker, as one goes up to high altitudes. By about $50$ kilometers, the field is very small, so most of the potential change (the integral of $E$) is at lower altitudes. The total potential difference from the surface of the earth to the top of the atmosphere is about $400{,}000$ volts.