If the current in a long straight wire doubles, what happens to the magnetic field at a fixed distance r?

If the current in a long straight wire doubles, what happens to the magnetic field at a fixed distance r?

• A. It quadruples
• B. It doubles
• C. It halves
• D. It remains the same

Answer: (B)

The magnetic field around a long straight wire scales directly with the current. The standard expression is B = μ0 I / (2π r), which shows that at a fixed distance r, B is proportional to I. So if the current doubles, the magnetic field at that distance doubles as well. The 1/r dependence means the field weakens with distance, but since r is fixed here, the change comes only from the current. If I changes by a factor, B changes by the same factor; doubling I simply doubles B.

The magnetic field around a long straight wire scales directly with the current. The standard expression is B = μ0 I / (2π r), which shows that at a fixed distance r, B is proportional to I. So if the current doubles, the magnetic field at that distance doubles as well. The 1/r dependence means the field weakens with distance, but since r is fixed here, the change comes only from the current. If I changes by a factor, B changes by the same factor; doubling I simply doubles B.