A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 7 A . The magnetic field at the centre of the solenoid is

• A

  $0.4396 \times 10^{-5} \mathrm{~T}$
• Correct answer
  B

  $4.396 \times 10^{-2} \mathrm{~T}$
• C

  $43.96 \times 10^{-2} \mathrm{~T}$
• D

  439.6 T

Solution

$\ell=1 \mathrm{~m} ; \mathrm{r}=2 \mathrm{~cm} ; \mathrm{N}=5000 ; \mathrm{t}=7 \mathrm{~A} ; \sin \theta \approx 1$
$\mathrm{B}=\frac{\mu_0 \mathrm{Ni}}{\ell} \sin \theta$ $\begin{aligned} & B=\frac{4 \pi \times 10^{-7} \times 5000 \times 7 \times 1}{1} \\ & B=4.396 \times 10^{-2} \mathrm{~T}\end{aligned}$

Hence, the correct answer is option: 'B'.