Final answer:
The magnetic field at point (2.0 m, 0, 0) caused by a long, straight wire carrying a 4.00-A current is directed counterclockwise around the z-axis when viewed from above, with a magnitude of 4×10-7 Tesla.
Step-by-step explanation:
The task is to find the magnetic field at a point in space due to a segment of current-carrying wire. We can solve this problem using the Biot-Savart Law or Ampère's Law. The Biot-Savart Law describes the magnetic field produced by a current element, while Ampère's Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. In this case, given the symmetry and the fact that we are dealing with a long, straight wire, Ampère's Law is more applicable.
The magnetic field direction at a point away from a current-carrying wire is given by the right-hand rule. Point your thumb in the direction of the current, and your fingers will curl in the direction of the magnetic field. At point (2.0 m, 0, 0), the magnetic field would circle around the z-axis in a counterclockwise direction when seen from above (from positive z towards negative z).
The magnitude of the magnetic field due to a long, straight wire is given by the formula B = (µ_0 * I) / (2 * π * r), where µ_0 is the permeability of free space (4π x 10-7 T*m/A), I is the current, and r is the radial distance from the wire. Plugging in the values, we get B = (4π x 10-7 T*m/A * 4 A) / (2 * π * 2 m) = 4×10-7 T.