Question

Two long straight wires are connected by a circular section which has a radius $R$ .All the three segments lie in the same plane and carry a current $I$. The magnetic induction at the centre $O$ of the circular segments is :

• A. $\frac{{\mu }_{0}I}{4\pi r}$
• B. $\frac{\alpha {\mu }_{0}I}{4\pi r}$
• C. $\frac{\alpha {\mu }_{0}I}{R}$
• D. $\frac{\alpha {\mu }_{0}I}{2\pi r}$

Answer 1

The correct option is B $\frac{\alpha {\mu }_{0}I}{4\pi r}$

magnetic field due to the wire$=0$
And CD & BA are passing through $O$
So due to straight wires $B=0$
$B$ due to circular arc$=\frac{{\mu }_{0}i}{4\pi r}\left(\theta \right)$
$=\frac{{\mu }_{0}i\alpha }{4\pi r}$