Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude $|\vec{B}|$ of the magnetic field
-(a) at point a?
A) $\mu_{0} / / 4 \pi R$
B) $\mu_{0} / / 2 \pi R$
C) $\mu_{0} I / \pi R$
D) $\mu_{0} l / R$
E) $(2+\pi) \mu_{0} / / 4 \pi R$
F) Zero

Question

Quizplus · Accepted Answer

The magnetic field at point a due to a straight wire segment is given by $\mu_{0} I / 4 \pi R$ for each side of the hairpin. The semicircular part contributes an additional $\mu_{0} I / 2 R$. Adding these contributions together gives $(2+\pi) \mu_{0} I / 4 \pi R$.

Consider a Wire Bent in the Hairpin Shape Shown Below ∣B⃗∣|\vec{B}|∣B∣

Consider a Wire Bent in the Hairpin Shape Shown Below $|\vec{B}|$