Question

Two long thin wires $ABC$ and $DEF$ are arranged as shown in figure. They carry equal current $I$ as shown. The magnitude of the magnetic field at $O$ is

• A. zero
• B. ${\mu }_{0}I/4\pi a$
• C. ${\mu }_{0}I/2\pi a$
• D. ${\mu }_{0}I/2\sqrt{2}\pi a$

Answer 1

The correct option is C ${\mu }_{0}I/2\pi a$

$AB$ and $DE$ do not give any magnetic field at $O$.
Magnetic field at a distance $d$ due to semi infinite wire is $B=\frac{{\mu }_{0}I}{4\pi d}$

Magnetic field at $O$ due to $BC$ is $B_{BC}=\frac{{\mu }_{0}I}{4\pi a}$ (out of plane of paper)
Magnetic field at $O$ due to $EF$ is

$B_{EF}=\frac{{\mu }_{0}I}{4\pi a}$ (out of plane of paper)

So the final $B$ is the sum of the BC and EF.

So, $B_{total}=B_{BC}+B_{EF}=\frac{{\mu }_{0}I}{2\pi a}$