Question

A wire of length $10cm$ is bent into an arc of a circle such that it subtends an angle of $1radian$ at the centre. If a current of $1A$ is passed through the wire, the magnetic induction at the centre of the circle will be :

• A. $2\pi \times {10}^{-4}T$
• B. $1\pi \times {10}^{-6}T$
• C. $1\pi \times {10}^{-4}T$
• D. $2\pi \times {10}^{-6}T$

Answer 1

Answer: (D)

$2\pi \times {10}^{-6}T$

Magnetic field due to any are subtending an angle $0^o$ is $B=\frac{{\mu }_{0}i}{4\pi r}\left(0\right)$
radius and length of are related as
$L=Rx$
$\frac{l}{2A}=\frac{r}{1}⟹r=\frac{10\times {10}^{-2}}{2\pi }$
$B=\frac{{10}^{-7}\times 2A}{0.1}\times 1$
= $2\pi \times {10}^{-6}T$