Question $6(1$ point$)$

A ferromagnetic material $($Fig$.$ A$)$ with a square cross$-$sectional area of $16c{m}^2$ has a relative permeability of $1000.$ The number of turns in the coil is $1000.$ The magnetic flux established in the core $($Fig$.$ A$)$ is $6\mathrm{.}4mWb.$ The above core is cut into equal halves and the one with the coil is extended with the same material as shown in Fig. B$.$ If the outer $($maximum$)$ circumference of the core in Fig. A is $52\mathrm{.}0$ cm$,$ the new number of turns in the coil required $($Fig$.$ B$)$ to produce the same magnetic flux of $6\mathrm{.}4mWb$ with same current as of Fig. A is $\_\_$

Fig.

A

Fig. Bturns.