The magnetic field around a long straight wire with current I is B = μ0 I /(2π r). How does B change with distance r from the wire?

The magnetic field around a long straight wire with current I is B = μ0 I /(2π r). How does B change with distance r from the wire?

• A. B ∝ r
• B. B ∝ 1/r
• C. B ∝ r^2
• D. B is independent of r

Answer: (B)

The key idea is that the magnetic field around a long straight wire falls off inversely with distance from the wire. The given expression B = μ0 I /(2π r) shows that r sits in the denominator, so as you move farther away, B decreases in proportion to 1/r. For example, doubling the distance halves the field. The constant μ0 I /(2π) just fixes the overall scale, but the way B changes with r is an inverse relationship. The field lines circle the wire, with direction given by the right-hand rule, but the magnitude’s dependence on distance is what’s being asked.

The key idea is that the magnetic field around a long straight wire falls off inversely with distance from the wire. The given expression B = μ0 I /(2π r) shows that r sits in the denominator, so as you move farther away, B decreases in proportion to 1/r. For example, doubling the distance halves the field. The constant μ0 I /(2π) just fixes the overall scale, but the way B changes with r is an inverse relationship. The field lines circle the wire, with direction given by the right-hand rule, but the magnitude’s dependence on distance is what’s being asked.