If a long straight wire's magnetic field distance is doubled, what happens to B?

If a long straight wire's magnetic field distance is doubled, what happens to B?

• A. It becomes quadruple
• B. It becomes half
• C. It becomes the same
• D. It becomes double

Answer: (B)

The magnetic field around a long straight current-carrying wire decreases inversely with distance from the wire. This comes from B = μ0 I / (2π r): as the distance r increases, the field strength falls off like 1/r. Doubling the distance means B is halved. So the field at twice the distance is half the original value. (If distance were halved, B would double.)

The magnetic field around a long straight current-carrying wire decreases inversely with distance from the wire. This comes from B = μ0 I / (2π r): as the distance r increases, the field strength falls off like 1/r. Doubling the distance means B is halved. So the field at twice the distance is half the original value. (If distance were halved, B would double.)