Answer:

The Maxwell equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields. These equations are named after the physicist James Clerk Maxwell and are the cornerstone of classical electromagnetism. The four Maxwell equations are:

1. Gauss's law for electric fields: This equation relates the flux of an electric field through a closed surface to the charge enclosed within that surface. It is given by:

∇ · E = ρ/ε₀

where ∇ · E is the divergence of the electric field E, ρ is the charge density, and ε₀ is the permittivity of free space. This equation does not involve the curl operation.

2. Gauss's law for magnetic fields: This equation relates the flux of a magnetic field through a closed surface to the magnetic monopole density inside that surface. It is given by:

∇ · B = 0

where ∇ · B is the divergence of the magnetic field B. This equation does not involve the curl operation.

3. Faraday's law of electromagnetic induction: This equation describes how a changing magnetic field induces an electric field. It is given by:

∇ × E = -∂B/∂t

where ∇ × E is the curl of the electric field E and ∂B/∂t is the time derivative of the magnetic field B. This equation involves the curl operation.

4. Ampere's law with Maxwell's addition: This equation relates the circulation of the magnetic field around a closed loop to the electric current and the displacement current. It is given by:

∇ × B = μ₀J + μ₀ε₀∂E/∂t

where ∇ × B is the curl of the magnetic field B, μ₀ is the permeability of free space, J is the electric current density, ∂E/∂t is the time derivative of the electric field E, and μ₀ε₀ is the product of the permeability and permittivity of free space. This equation involves the curl operation.

From the above explanations, we can see that the third and fourth Maxwell equations involve the curl operation. Therefore, the correct answer is option 'A' - only Maxwell's first and second equations do not involve the curl operation.