Final answer:
The magnetic field around a long straight wire carrying current I is given by B = (µ₀I)/(2πR), and it is inversely proportional to the distance R from the wire. Therefore, as the distance from the wire changes to 2r, r/2, r/√2, and 2r/√2, the magnetic fields are calculated as 0.25 T, 1 T, approximately 0.71 T, and approximately 0.35 T, respectively.
Step-by-step explanation:
The magnetic field created by a current in a long straight wire is governed by Ampère's law, which relates the magnetic field around a conductor to the current it carries. According to Ampère's law, the magnetic field (B) at a distance (R) from a long straight conductor is given by:
B = (µ0I)/(2πR),
where µ0 is the permeability of free space, I is the current, and R is the distance from the wire. Since the magnetic field at a distance r is 0.5 T, we can relate the magnetic field at other distances using this formula, understanding that the magnetic field is inversely proportional to the distance from the conductor. For each of the different distances questioned, the magnetic field strength would be:
- a) 2r: B is 0.25 T (since doubling the distance r halves the magnetic field).
- b) r/2: B is 1 T (since halving the distance r doubles the magnetic field).
- c) r/√2: B is approximately 0.71 T (since the distance is multiplied by √2, the magnetic field is divided by √2).
- d) 2r/√2: B is approximately 0.35 T (since the distance is multiplied by 2/√2, which is equal to √2, the magnetic field is divided by √2).
It is important to note that we are assuming here that the distances do not go beyond the region where the magnetic field due to the wire could be considered practically uniform and the wire is viewed as 'infinitely' long.