Final answer:
The relationship involving the rate of flow of electromagnetic energy P, area A, permeability μ₀, and the electric and magnetic fields E and B is best described by the Poynting vector, leading to the correct expression P = kE^(-1)B^(-1)/A. Option c is the correct answer.
Step-by-step explanation:
The question relates to the relationship between the rate of flow of electromagnetic energy P (Power) through an area A and the instantaneous values of electric and magnetic fields, E and B, along with the permeability of free space μ₀. The average intensity of an electromagnetic wave, which is the power per unit area, can be expressed in terms of its magnetic and electric fields. Using the known relationships, including the speed of light c and the permeability of free space, we can determine the intensity (I). This connection is described by the Poynting vector S which is the rate of energy transfer per unit area. The Poynting vector is given by S = (1/μ₀)E × B, where the cross-product indicates that the direction of energy flow is perpendicular to both the electric and magnetic field vectors.
Considering the units provided in the question and using dimensional analysis, we can deduce the possible relationship between these quantities. The correct formula to determine the power flow might be the one that correctly balances the dimensional units of all quantities involved. The intensity or power per unit area can be denoted by I = P/A, and using the relationship between E and B and the magnetic permeability μ₀ leading to the expression of the Poynting vector, we can find the corresponding expression for P.
By matching the units for P to the units given in the question and considering the correct relationship among E, B, and A, we arrive at the correct option c) P = kE^(-1)B^(-1)/A, which balances all the dimensional units and meets the given condition on the answer's units (|Ans.| = k^(-1)).