What is the magnetic field magnitude around a long straight wire carrying current I at distance r, and what is its direction?

What is the magnetic field magnitude around a long straight wire carrying current I at distance r, and what is its direction?

• A. B = μ0 I /(2π r); direction azimuthal around the wire (right-hand rule)
• B. B = μ0 I r /(2π); direction radial
• C. B = μ0 I /(2 r); direction tangential
• D. B = μ0 I /(2π r^2); direction azimuthal

Answer: (A)

Magnetic field around a long straight current-carrying wire forms circles centered on the wire, and its strength decreases as 1/r with distance r from the wire. This result comes from Ampere’s law: for a circular Amperian loop of radius r coaxial with the wire, the line integral ∮ B · dl equals μ0 I. Since B is tangent to the loop and has constant magnitude along it, you get B(2πr) = μ0I, so B = μ0I/(2πr). The direction is tangential to these circles, which means it goes around the wire. The right-hand rule tells you that if you point your thumb along the current, your fingers curl in the direction of the magnetic field around the wire. So the field magnitude is μ0I/(2πr) and it points azimuthally (tangentially) around the wire.

Magnetic field around a long straight current-carrying wire forms circles centered on the wire, and its strength decreases as 1/r with distance r from the wire. This result comes from Ampere’s law: for a circular Amperian loop of radius r coaxial with the wire, the line integral ∮ B · dl equals μ0 I. Since B is tangent to the loop and has constant magnitude along it, you get B(2πr) = μ0I, so B = μ0I/(2πr).

The direction is tangential to these circles, which means it goes around the wire. The right-hand rule tells you that if you point your thumb along the current, your fingers curl in the direction of the magnetic field around the wire.

So the field magnitude is μ0I/(2πr) and it points azimuthally (tangentially) around the wire.