JEE MAIN - Physics (2023 - 24th January Evening Shift - No. 3)
A long solenoid is formed by winding 70 turns cm$$^{-1}$$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($$\mu_0=4\pi\times10^{-7}$$ TmA$$^{-1}$$)
$$88\times10^{-4}$$ T
$$1232\times10^{-4}$$ T
$$176\times10^{-4}$$ T
$$352\times10^{-4}$$ T
Explanation
Number of turns per meter $=7000$ turns per $\mathrm{m}$
$$ \begin{aligned} &i=2 \mathrm{~A} & \\\\ & B=\mu_{0} n i =4 \pi \times 10^{-7} \times 7000 \times 2 \\\\ & =56 \pi \times 10^{-4} \mathrm{~T} \\\\ & =56 \times \frac{22}{7} \times 10^{-4} \mathrm{~T} \\\\ & =176 \times 10^{-4} \mathrm{~T} \end{aligned} $$
$$ \begin{aligned} &i=2 \mathrm{~A} & \\\\ & B=\mu_{0} n i =4 \pi \times 10^{-7} \times 7000 \times 2 \\\\ & =56 \pi \times 10^{-4} \mathrm{~T} \\\\ & =56 \times \frac{22}{7} \times 10^{-4} \mathrm{~T} \\\\ & =176 \times 10^{-4} \mathrm{~T} \end{aligned} $$
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