Question

There are $1000$ turns per $5cm$ length in very long solenoid. It carries a current of $5A$. The magnetic field at its centre on the axis is _______ T

• A. $3.14\times {10}^{-2}T$
• B. $9.42\times {10}^{-2}T$
• C. $6.28\times {10}^{-2}T$
• D. $12.14\times {10}^{-2}T$

Answer 1

The correct option is D $12.14\times {10}^{-2}T$

No. of turns , N$=1000$ , l$=5cm=0.05m$

$n=\frac{N}{L}=\frac{1000}{0.05}=\frac{200}{100}=2$

$I=5A$

Magnetic field at its center , B$={\mu }_{0}nI$

$=4\pi \times {10}^{-7}\times 5T$

$=4000\times \pi \times {10}^{-7}T=4\times 3.14\times {10}^{-2}T$

$=12.14\times {10}^{-2}T$