Final answer:
The question is about the electric field associated with a given magnetic field in an electromagnetic wave. The correct electric field corresponds to B₀ sin(ky - ωt)ˇ, meaning the wave's electric and magnetic fields are in phase, perpendicular to each other, and travel in the positive y direction.
Step-by-step explanation:
The question involves a plane electromagnetic wave traveling in a vacuum, which is characterized by oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. The magnetic field of the wave is given by B(y, t) = B₀ sin(ky - ωt)î. According to Maxwell's equations and the properties of electromagnetic waves, the associated electric field would also oscillate with the same frequency and wavenumber but would be oriented perpendicular to both the magnetic field and the direction of propagation.
The correct answer to which field corresponds to the given magnetic field is: E(y,t) = B₀ sin(ky - ωt)ˇ, which means option (a) is the associated electric field. This conclusion is based on the fact that electric and magnetic fields in a plane electromagnetic wave are in phase and perpendicular to each other.
The amplitude of the wave is B₀, the frequency can be determined from the angular frequency ω, the wavenumber k is related to the wavelength λ by the equation k = 2π / λ, and the direction of travel of the wave can be deduced from the argument of the sinusoidal function (ky - ωt) indicating propagation in the positive y direction.