Question

A wire of length $10cm$ is bent into an arc of a circle such that it subtends an angle of $1$ radian 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. $2\times {10}^{-4}$ tesla
• B. $1\times {10}^{-6}$ tesla
• C. $1\times {10}^{-4}$ tesla
• D. $2\pi \times {10}^{-6}$ tesla

Answer 1

The correct option is B $1\times {10}^{-6}$ tesla

Given,

$\theta =1^0$

$I=1A$

From the figure,

$R=\frac{10cm}{\theta }=\frac{10cm}{1}=10cm=0.10m$

The magnetic field at the center is given by

$B=\frac{{\mu }_{0}I\theta }{4\pi R}$

$B=\frac{4\pi \times {10}^{-7}\times 1\times 1}{4\pi \times 0.10}T$

$B=1\times {10}^{-6}T$

The correct option is B.