The SI unit of the magnetic field, as derived from the Biot-Savart law, is the Tesla (T).

Explanation:
1. Introduction to the Biot-Savart Law:
The Biot-Savart law is a fundamental principle in electromagnetism that describes the magnetic field produced by a current-carrying wire. It states that the magnetic field at a point in space is directly proportional to the current flowing through the wire and inversely proportional to the distance from the wire.

2. The Equation of the Biot-Savart Law:
The Biot-Savart law can be mathematically expressed as:
B = (μ0 / 4π) * (I * dl x r) / r^3
where:
- B is the magnetic field at a point,
- μ0 is the permeability of free space (a constant value),
- I is the current flowing through the wire,
- dl is an infinitesimally small length element of the wire,
- r is the displacement vector from the length element to the point of interest.

3. SI Unit of Current:
The SI unit of electric current is the Ampere (A). One Ampere is defined as one Coulomb of charge passing through a point in one second.

4. SI Unit of Permeability of Free Space:
The permeability of free space, μ0, has a value of approximately 4π x 10^-7 T·m/A. It is a constant in the Biot-Savart law equation.

5. SI Unit of Magnetic Field:
By rearranging the Biot-Savart law equation, we find that the magnetic field is measured in Tesla (T):
B = (μ0 / 4π) * (I * dl x r) / r^3
B = (μ0 * I * dl x r) / (4π * r^3)

6. Definition of Tesla:
One Tesla is defined as one Newton per Ampere per meter (N/A·m). It represents a magnetic field such that a wire carrying a current of one Ampere experiences a force of one Newton per meter of length perpendicular to the magnetic field.

Therefore, the SI unit of magnetic field derived from the Biot-Savart law is the Tesla (T).