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A solenoid is $2 \mathrm{~m}$ long and $3 \mathrm{~cm}$ in diameter. It has 5 layers of winding of 1000 turns each and carries a current of $5 \mathrm{~A}$. What is the magnetic field at its centre ? Use the standard value of $\mu_{0}$.
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Verified Answer
The correct answer is:
$1.57 \times 10^{-2} \mathrm{~T}$
Length of solenoid, $l=2 \mathrm{~m}$
Total number of turns, $\mathrm{N}=5 \times 1000=5000$
Number of turns per unit length,
$\mathrm{n}=\frac{\mathrm{N}}{l}=\frac{5000}{2}=2500 \mathrm{~m}^{-1}$
Current, I = 5A
Now, B $=\mu_{0} \mathrm{nI}=4 \pi \times 10^{-7} \times 2500 \times 5 \mathrm{~T}$
$=1.57 \times 10^{-2} \mathrm{~T}$
Total number of turns, $\mathrm{N}=5 \times 1000=5000$
Number of turns per unit length,
$\mathrm{n}=\frac{\mathrm{N}}{l}=\frac{5000}{2}=2500 \mathrm{~m}^{-1}$
Current, I = 5A
Now, B $=\mu_{0} \mathrm{nI}=4 \pi \times 10^{-7} \times 2500 \times 5 \mathrm{~T}$
$=1.57 \times 10^{-2} \mathrm{~T}$
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