Final answer:
The ratio of the magnetic field at 7.5 cm to 50 cm from a long straight current-carrying conductor is approximately 6.7:1. There might be an error in the options listed
Step-by-step explanation:
The question is asking about the magnetic field produced by a long straight current-carrying conductor at different distances. According to Ampère's law, the magnetic field (B) at a distance r from a long straight conductor carrying current I is given by B = μ0I/(2πr), where μ0 is the permeability of free space. This formula shows that the magnetic field is inversely proportional to the distance from the wire, meaning that if you increase the distance, the magnetic field strength decreases, and vice versa.
Therefore, to find the ratio of the magnetic field at a distance of 7.5 cm (r1) to that at 50 cm (r2), we use the inverse proportionality:
B1/B2 = r2/r1
Plugging in the distances:
B1/B2 = 50 cm / 7.5 cm = 6.67, which simplifies to approximately 6.7:1, which is not one of the options provided in the question. There might be an error in the options listed, or additional information may be needed to match one of the given choices.