Final answer:
Magnetic field vectors can be obtained from changing magnetic fields using Faraday's law by calculating the magnetic flux, obtaining the induced emf, and then using Ohm's law to find the current. Lenz's law tells us the direction of current that opposes the change in magnetic flux.
Step-by-step explanation:
To obtain magnetic field vectors from electric field vectors using Faraday's law of electromagnetic induction, we must consider the relationship between changing magnetic flux and induced electromotive force (emf). First, we calculate the magnetic flux (Φ) through a surface by taking the product of the strength of the magnetic field (B), the surface area (A), and the cosine of the angle (θ) between the normal to the surface and the magnetic field. Faraday's law states that the magnitude of induced emf in a closed loop is equal to the negative rate of change of magnetic flux through the loop (Φ), or E = -dΦ/dt.
By applying Ohm's law, once we have the induced emf, we can calculate the current (I) in the circuit, where I = E/R, with R being the resistance. To determine the direction of the induced current, we use Lenz's law, which tells us that the induced current will create a magnetic field opposing the change in the original magnetic flux.
This process does not reverse to give us the original electric field, but it provides insight into the dynamics between changing magnetic fields and electric currents in a circuit. It's worth noting that we started from the induced emf from a changing magnetic field rather than directly from electric field vectors.