Final answer:
The contribution of the short wire segment to the magnetic field is zero.
Step-by-step explanation:
To find the contribution of the short segment of the wire to the magnetic field at point B, we can use the Biot-Savart Law. The Biot-Savart Law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and the length of the wire segment, and inversely proportional to the distance from the wire.
In this case, we know the current (i = 6.00 A), the length of the wire segment (l = 4.00 mm), and the distance from the wire (r = d = 0, since the wire is centered at the origin).
Using the Biot-Savart Law, we can calculate the magnetic field contribution b:
b = (μ₀ i l)/(4πr)
Where μ₀ is the permeability of free space and has a value of 4π x 10⁻⁷ T·m/A.
Substituting the given values, we get:
b = (4π x 10⁻⁷ T·m/A x 6.00 A x 4.00 x 10⁻³ m) / (4π x 0 m)
Simplifying, we find that the contribution b is equal to zero.