The magnetic field produced by a current carrying wire is given by Ampere's law and its direction is determined by the right-hand thumb rule.
(a) For the point (2.00 m, 0, 0), we first need to calculate the magnetic field using the formula:
B = μIΔL / 2πr
Where:
- μ is the permeability of free space, which equals 4π * 10^-7 T*m/A
- I is the current in the wire, which equals 4 A
- ΔL is the segment length of the wire, which equals 0.500 * 10^-3 m
- r is the distance from the wire, equal to 2 m in this case
Plugging these values into the formula gives us the magnitude of the magnetic field. Based on the right-hand rule, because the current is in the +z direction, the magnetic field at this point is in the -y direction.
(b) For point (0, 2.00 m, 0) we apply the same method as above, but the distance from the wire is now 2 m in the y direction. Inserting these values into the formula will give us the strength of the magnetic field. According to the right-hand rule, the direction at this point will be in the +x direction.
(c) For point (2.00 m, 2.00 m, 0), the distance from the wire is different than the previous points. We use Pythagoras' theorem to find the distance, r = √[(2^2) + (2^2)]. The direction, according to the right-hand rule with current in the +z direction, must be towards the origin.
(d) For point (0, 0, 2.00 m) the segment of the wire and the point are aligned along the z-axis. Theoretically, for a point located along the axis of a current-carrying wire, the magnetic field should be zero. Therefore, we can say that the magnetic field at this point is non-existent or null.