Q148 / 160 · TS EAMCET 2023 (13 May Shift 2) · Physics
A closely wound solenoid of $80 \mathrm{~cm}$ long has 5 layers of windings of 400 turns each. The diameter of the solenoid is $1.8 \mathrm{~cm}$. If the current carried is $8 \mathrm{~A}$, then the magnitude of the magnetic field inside the solenoid near its centre is approximately
- A$1.5 \times 10^{-2} \mathrm{~T}$
- Correct answerB$2.5 \times 10^{-2} \mathrm{~T}$
- C$3.5 \times 10^{-2} \mathrm{~T}$
- D$4.5 \times 10^{-2} \mathrm{~T}$
Solution
Length of Solenoid, $\mathrm{L}=80 \mathrm{~cm}=0.8 \mathrm{~m}$ Diameter of a solenoid, $\mathrm{d}=1.8 \mathrm{~cm}=0.018 \mathrm{~m}$
Current, $\mathrm{i}=8 \mathrm{~A}$
Total number of turns. $\mathrm{N}=5 \times 400=2000$
Number of turns per unit length $\mathrm{n}=\frac{\mathrm{N}}{\mathrm{L}}$
$$
\begin{aligned}
& =\frac{2000}{0.8} \\
& =2500
\end{aligned}
$$
Magnetic field at the centre of solenoid
$$
\begin{aligned}
& \mathrm{B}=\mu_0 \mathrm{ni} \\
& =4 \pi \times 10^{-7} \times 2500 \times 8 \\
& =2.5 \times 10^{-2} \mathrm{~T}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.