What is the expression for the magnetic field at a distance r from a long straight current I?

What is the expression for the magnetic field at a distance r from a long straight current I?

• A. B = μ0 I r / 2π
• B. B = μ0 I / (π r)
• C. B = μ0 I / 2π r
• D. B = 2π μ0 I / r

Answer: (C)

When a current runs through a long straight wire, the magnetic field forms circular lines around the wire. To find its strength at a distance r, apply Ampere’s law with a circular path of radius r centered on the wire. The line integral of B around that loop equals μ0 times the enclosed current: ∮B·dl = μ0 I. The field is tangential and has the same magnitude at every point on the circle, so ∮B·dl = B(2πr). Solving gives B = μ0 I /(2πr). The direction is around the wire following the right-hand rule: if the current is upward, the field circles counterclockwise. The 1/r dependence shows the field weakens with distance.

When a current runs through a long straight wire, the magnetic field forms circular lines around the wire. To find its strength at a distance r, apply Ampere’s law with a circular path of radius r centered on the wire. The line integral of B around that loop equals μ0 times the enclosed current: ∮B·dl = μ0 I. The field is tangential and has the same magnitude at every point on the circle, so ∮B·dl = B(2πr). Solving gives B = μ0 I /(2πr). The direction is around the wire following the right-hand rule: if the current is upward, the field circles counterclockwise. The 1/r dependence shows the field weakens with distance.