Let's proceed step by step:
1. We first take the given diameter of the laser beam which is 2.00 mm or 2.00e-3 meters. The radius of the beam will be half of its diameter, i.e., 1.00e-3 meters.
2. The given B-field's rms strength is 8.33e-11 teslas.
3. We will also need the speed of light which is roughly 3e8 meters per second and the permeability of free space, denoted by 'μ', which is approximately equal to 4πe-7 henry per meter.
4. Now, we calculate the power of the beam. This is done by substituting the given values into the formula for the power P of a laser beam, which states that P = (0.5 * B^2 / μ) * (π * r^2) * c. On substituting our values, we get P = 2.60e-12 watts.
5. Then, to calculate the total energy transported by the beam per hour, we multiply the power by the number of seconds in an hour, which is 3600 seconds. Doing this gives us the total energy transported per hour as 9.37e-9 joules.
So, contrary to the initial assumption, the total power in the laser beam is 2.60e-12 watts and the total energy transported per hour along the beam is 9.37e-9 joules.