A field can exist if it satisfiesSelect one:a. Gauss Lawb. All Maxwell's equationsc. Coulumb's Lawd. Faraday's Law

To determine if a field exists, we need to consider the conditions that must be satisfied.

First, let's look at Gauss's Law. Gauss's Law states that the total electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of the medium. This law relates the electric field to the charge distribution. So, satisfying Gauss's Law is one condition for the existence of a field.

Next, we have Maxwell's equations. Maxwell's equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields. These equations include Gauss's Law for electric fields, Gauss's Law for magnetic fields, Faraday's Law of electromagnetic induction, and Ampere's Law with Maxwell's addition. All of these equations are necessary to fully describe the behavior of fields. Therefore, satisfying all of Maxwell's equations is another condition for the existence of a field.

Now, let's consider Coulomb's Law. Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. While Coulomb's Law is important in understanding the behavior of electric fields, it alone is not sufficient to determine the existence of a field. Therefore, satisfying Coulomb's Law is not a standalone condition for the existence of a field.

Lastly, we have Faraday's Law of electromagnetic induction. Faraday's Law states that a changing magnetic field induces an electromotive force (EMF) in a closed loop of wire. This law relates the magnetic field to the induced electric field. While Faraday's Law is crucial in understanding the behavior of electromagnetic fields, it alone is not sufficient to determine the existence of a field. Therefore, satisfying Faraday's Law is not a standalone condition for the existence of a field.

In conclusion, to determine if a field exists, it must satisfy both Gauss's Law and all of Maxwell's equations. Therefore, the correct answer is option b. All Maxwell's equations.