It might be useful to take a simple look at simple antennas. This should give us some insight into more complicated structures. Remember, some things that apply to simple structures will also apply to complex ones.
The Isotropic Radiator
An isotropic radiator is one that radiates uniformly in all directions. Not to physically realizable, huh? Think of a light bulb. Oops, that's got a "null" toward its base. Well, most radiators have a null or two somewhere in their patterns. That's what they call them ... patterns. That's a graph or plot of where the radiated power goes. Azimuth patterns ... elevation patterns .... Well, anyway, an isotropic radiator radiates equally well in all directions; it's pattern is like a beach ball around the antenna. Or it's azimuth pattern and elevation pattern are just circles.
The important thing to remember about antennas is that the power W that is radiated is passing through that beach ball ... all of it. For a ball of radius R, the surface area is 4*PI*R^2, so the Power Density at the surface is
P = W / (4*PI*R^2).
Now the Poynting Vector P (that's what it's called) points in the direction of the power flow, in this case, out from the radiator. Notice that the power density goes down as inverse square of the distance away from the radiator. We can also show (but I won't here) that
P = E x H and P = E^2 / Zfs
where Zfs is the intrinsic impedance of the medium (like the air at 377) in ohms per square and E is the electric field and H is the magnetic field.
We could combine these relations, eliminating P, and find that the electric field a distance R from an isotropic radiator of power W is
E = (1 / R) * (Zfs * W / 4 / PI) ^ 0.5
if I did my algebra right.
Gain
Now dipoles, because they radiate more power in some directions and less in others, have a gain of 1.6 or so, or 2 dB above an isotropic antenna. Verticals over a good conductor radiate all their power in a half-space (not into the ground) and usually have another factor of 2, or 3 dB of "gain". In their preferred directions, antennas over good ground (like a mirrored surface) have at most 6 dB of additional gain.
Examples
1. What is the electric field 10 meters from an isotropic antenna in free space (far from anything else) radiating 100 watts?
E = (1/10)*(377*100/4/3.14)^0.5 = 5.5 volts/meter
2. Example 1, but the antenna is a quarter wave ground-mounted vertical?
E = (1/10)*(377*100*1.6*2/4/3.14)^0.5 = 10 volts/meter.
By the way, a wire 1 meter long and oriented in the direction of the electric field would have an open-circuit voltage across it of 10 volts. And you wonder why hams get into TVs, radios, and appliances?
Assumptions
There are tons of them, like, the observation point is in the "far-field" of the antenna, and the ground is ideal, and the conductors are lossless. But, at least you can get a good idea of where you are with a simple analysis. Any way, stay-tuned ... there's more to come.