State the four Maxwell equations for an electric field, E, and a magnetic field, B (you do notneed to define other symbols used).

The four Maxwell's equations are:

1. Gauss's Law for Electricity: This law states that the electric flux through any closed surface is equal to 1/ε₀ times the total charge enclosed by that surface. Mathematically, it is represented as ∮E.dA = Q/ε₀.

2. Gauss's Law for Magnetism: This law states that the net magnetic flux through any closed surface is zero. This is because magnetic fields are dipolar, they have both a north and south pole. Mathematically, it is represented as ∮B.dA = 0.

3. Faraday's Law of Electromagnetic Induction: This law states that a time-varying magnetic field will induce an electromotive force (EMF) in a closed loop of wire. Mathematically, it is represented as ∮E.dl = -d(∮B.dA)/dt.

4. Ampere's Law with Maxwell's Addition: This law states that magnetic fields can be generated in two ways: by electric current (Ampere's Law) and by changing electric fields (Maxwell's Addition). Mathematically, it is represented as ∮B.dl = μ₀I + μ₀ε₀(d(∮E.dA)/dt).

Here, E is the electric field, B is the magnetic field, dA is a differential area, dl is a differential length, Q is the total charge, I is the current, ε₀ is the permittivity of free space, μ₀ is the permeability of free space, and t is time.