Final answer:
Option (d) ∇×B=μ_0J is technically not incorrect for a static field; it simply lacks the displacement current term which wouldn't be present in a static scenario. Hence, all provided options apply to static fields and fit within Maxwell's equations for static scenarios in a linear homogeneous medium.
Step-by-step explanation:
The question pertains to Maxwell's equations in the context of a static electromagnetic field in a linear homogeneous medium. Maxwell's equations describe how electric fields (E) and magnetic fields (B) interact and propagate as electromagnetic waves. These equations can be summarized as follows:
- Gauss's law for electricity: ∇⋅E=ε_0 (the electric flux out of a closed surface is proportional to the enclosed charge)
- Gauss's law for magnetism: ∇⋅B=0 (the magnetic flux out of a closed surface is zero, indicating no magnetic monopoles)
- Faraday's law of induction: ∇×E=-∂B/∂t (a changing magnetic field induces an electric field)
- Ampère's law (with Maxwell's addition): ∇×B=μ_0 J + μ_0 ε_0 ∂E/∂t (magnetic fields are generated by currents and changing electric fields)
Among the given options (a, b, c, d), option (d) ∇×B=μ_0J is not one of Maxwell's equations for a static field. This is because it lacks the displacement current term μ_0 ε_0 ∂E/∂t, which is necessary for Maxwell's equations during dynamic conditions, such as the propagation of electromagnetic waves. In the static case, however, the displacement current term would be zero and the given equation would be correct. Therefore, all options given apply to static fields, not distinguishing between them in this context.