For a finite straight wire segment at distance d with θ1 = 0 and θ2 = π, what is the magnitude of the magnetic field B at that distance?

For a finite straight wire segment at distance d with θ1 = 0 and θ2 = π, what is the magnitude of the magnetic field B at that distance?

• A. B = μ0 I /(4π d)
• B. B = μ0 I /(2 d)
• C. B = μ0 I /(π d)
• D. B = μ0 I /(2π d)

Answer: (D)

The magnetic field from a finite straight wire depends on the geometry of the ends as seen from the point, and the Biot–Savart law gives the magnitude B = (μ0 I)/(4π d) [cos θ1 − cos θ2], where θ1 and θ2 are the angles from the wire’s ends to the observation point measured relative to the wire’s direction. Here, the angles are 0 and π, so cos 0 = 1 and cos π = −1. Substituting yields B = (μ0 I)/(4π d) [1 − (−1)] = (μ0 I)/(2π d). The magnetic field circles the wire in a direction given by the right-hand rule.

The magnetic field from a finite straight wire depends on the geometry of the ends as seen from the point, and the Biot–Savart law gives the magnitude B = (μ0 I)/(4π d) [cos θ1 − cos θ2], where θ1 and θ2 are the angles from the wire’s ends to the observation point measured relative to the wire’s direction. Here, the angles are 0 and π, so cos 0 = 1 and cos π = −1. Substituting yields B = (μ0 I)/(4π d) [1 − (−1)] = (μ0 I)/(2π d). The magnetic field circles the wire in a direction given by the right-hand rule.