Question

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

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

Answer 1

The correct option is C

$\frac{{\mu }_{0}I}{2\pi a}$
The magnetic field due to wires AB and DE at the origin will be zero.

Magnetic field at O due to wire BC, $B_{BC}=\frac{{\mu }_{0}I}{4\pi a}⨀$

Magnetic field at O due to wire EF, $B_{EF}=\frac{{\mu }_{0}I}{4\pi a}⨀$

Net magnetic field at O, $B=B_{BC}+B_{EF}=\frac{{\mu }_{0}I}{4\pi a}+\frac{{\mu }_{0}I}{4\pi a}=\frac{{\mu }_{0}I}{2\pi a}$

Hence, the correct answer is option (c).