Question

A current carrying conductor of length l is bent into two loops one by one. First loop has one turn of wire and the second loop has two turns of wire. Compare the magnetic fields at the center of the loops.

Answer 1

In first case, $l=2\pi r_1$; In second case,$l=2\times \left(2\pi r_2\right)\Rightarrow r_2=\frac{r_1}{2}$
At centre, $B=\frac{{\mu }_{0}i}{2r_1}$ $B^{\prime }=\frac{2\times {\mu }_{0}i}{2r_2}$ ($\because$ there are 2 turns )
$\Rightarrow \frac{B^{\prime }}{B}=\frac{2r_1}{r_2}=4$
$\therefore B^{\prime }=4B$