Physics - Magnetism Question with Solution | TestHub

Let's assume that the current in the coil is Initially the field at the centre is $i$ and the radius of the coil is $r$, then the initial magnetic field at the centre is

$B_{\mathrm{initial}}=\frac{{\mu }_{0}i}{2r}$

When we make two loops out of one, we are basically making a coil of half the radius and double the number of turns, so

$$\begin{gathered} B_{\mathrm{final}}=2\frac{{\mu }_{0}i}{2\left(\raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}=\frac{2{\mu }_{0}i}{r} \\ \Rightarrow B_{\mathrm{final}}=4B_{\mathrm{initial}}=4B \end{gathered}$$