No, the intensity of an electromagnetic (EM) wave falling off as the square of its distance from its source does not imply that its energy and power fall off even faster than that. In fact, the energy and power of an EM wave also follow the inverse square law.
Let's consider the relationship between intensity, energy, power, and distance for an EM wave. Intensity (I) is defined as the power (P) per unit area (A):
I = P / A
The power of the wave (P) is the rate at which energy is transmitted by the wave. Energy (E) is given by the product of power and time:
E = P * t
Now, let's examine how intensity, energy, and power change with distance (r). Assuming the wave is spreading uniformly in all directions, the intensity is inversely proportional to the square of the distance:
I ∝ 1 / r^2
Since intensity is power divided by area, and the area of a sphere increases with the square of the radius, the intensity falls off as 1/r^2.
Now, let's look at energy and power. The power transmitted by the wave does not change with distance since the rate at which energy is transmitted remains constant. Therefore, the power does not decrease as the wave propagates.
The energy transmitted by the wave, on the other hand, is distributed over an increasing area as the wave expands. The energy density (energy per unit volume) decreases with the square of the distance:
Energy density ∝ 1 / r^2
However, the total energy transmitted by the wave is conserved. So, while the energy density decreases as 1/r^2, the total energy remains constant as the wave spreads out.
In summary, the intensity of an EM wave falling off as the square of the distance from its source indicates that the energy density decreases as 1/r^2, but the total energy and power transmitted by the wave remain constant as long as no energy is absorbed or dissipated along the way.