To solve this problem, we can use the formula for flux density, which is given by the equation:
S = P/4πr^2
Where S is the flux density, P is the power radiated by the source, and r is the distance from the source.
In this case, we are given that the power radiated by the source is 100 W and the distance from the source is 1 m. Plugging in these values into the formula, we get:
S = 100/4π(1)^2 = 25/π W/m^2
This means that the flux density at a distance of 1 m from the source is approximately 7.9577 W/m^2.
To find the amplitudes of the E and B fields at this point, we can use the formula:
S = (1/2)√(ε0/μ0)E0^2
Where S is the flux density, ε0 and μ0 are the permittivity and permeability of free space respectively, and E0 is the amplitude of the electric field.
To solve for E0, we rearrange the formula to get:
E0 = √(2Sμ0/ε0)
Plugging in the values for S, μ0, and ε0, we get:
E0 = √(2(7.9577)(4π x 10^-7)/(8.854 x 10^-12)) = 5.6719 x 10^-3 V/m
Similarly, we can find the amplitude of the magnetic field using the formula:
S = (1/2)√(ε0/μ0)B0^2
Rearranging the formula and plugging in the values, we get:
B0 = √(2Sε0/μ0) = √(2(7.9577)(8.854 x 10^-12)/(4π x 10^-7)) = 3.1834 x 10^-9 T
Therefore, the amplitudes of the E and B fields at a distance of 1 m from the source are approximately 5.6719 x 10^-3 V/m and 3.1834 x 10^-9 T, respectively.
In summary, to solve this flux density problem, we used the formula for flux density and the formulas for the amplit