Final answer:
Ampere's law can be applied by considering a circular path within the wire and calculating the current passing through the area enclosed by the path. The magnetic field can be determined by evaluating the line integral of the magnetic field along the path.
Step-by-step explanation:
Maxwell-Ampere's law relates the integral of the magnetic field around a closed loop to the net current passing through any surface bounded by the loop. In the given situation, the current density is given as J⃗ =IAk^, and assuming there is no displacement current, Ampere's law can be applied.
The constant current density J⃗ =IAk^ denotes a current flowing in the z-direction in a wire. To apply Ampere's law, we consider a circular path within the wire (r ≤ a) and calculate the current I passing through the area enclosed by the path. This is done by multiplying the current density J with the area enclosed. Since the current is uniform, the current density inside the path is equal to the current density in the whole wire, which is Io/a². Therefore, the current I passing through the area enclosed by the path is given as Пр2 I = Io παζ.
Using Ampere's law, which relates the magnetic field (B) to the current (I) passing through any surface enclosed by a loop, we can determine the magnetic field created by the constant current density. By evaluating the line integral of the magnetic field along the path, we can calculate the magnetic field strength at various points.