Question

A thin uniform wire is bent in the form as shown in the figure without touching at any point ABCD in a circular loop of radius r. If current I is sent through the wire, the magnetic induction at the centre O of the loop is?

• A. $\frac{{\mu }_{0}I}{r}$
• B. $\frac{{\mu }_0}{2r}(1+\frac{1}{\pi })$
• C. $\frac{{\mu }_{0}I}{2r}\cdot (1+\frac{1}{\pi })$
• D. $\frac{2{\mu }_{0}I}{r}$

Answer 1

The correct option is C $\frac{{\mu }_{0}I}{2r}\cdot (1+\frac{1}{\pi })$

The field at O due to straight part of wire $B_1=\frac{{\mu }_{o}I}{2\pi r}$

The field at O due to circualr part of wire $B_1=\frac{{\mu }_{o}I}{2r}$

Both the fields are in the same direction that is into the plane .

Hence net field $B=B_1+B_2$

$⟹B=\frac{{\mu }_{o}I}{2r}(1+\frac{1}{\pi })$

Answer-(C)