A long solenoid is fabricated to closely winding wire of radius $0.5\,mm$ over a cylindrical frame so that the successive turns nearly touch each other, the magnetic field at the centre of solenoid if it carries a current of $5\,A$
Medium
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$\Rightarrow \quad \mathrm{B}=\mu_{0} \frac{\mathrm{N}}{\mathrm{L}} \times \mathrm{I}$
$\mathrm{N} \times 2 \mathrm{r}=\mathrm{L} \quad(\mathrm{r}=\text { radius of wire })$
so $\frac{\mathrm{N}}{\mathrm{L}}=\frac{1}{2 \mathrm{r}}$
$\Rightarrow \quad B=\frac{\mu_{0} I}{2 r}$
$B=\frac{4 \pi \times 10^{-7} \times 5 \times 10^{3}}{2 \times 0.5}$
$\mathrm{B}=20 \pi \times 10^{-4}\, \mathrm{T}$
$\mathrm{B}=2 \pi \times 10^{-3} \,\mathrm{T}$
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