A closely wound solenoid of length $1 \mathrm{~m}$ has 5 layers of 500 turns each. If the magnitude of…

A closely wound solenoid of length $1 \mathrm{~m}$ has 5 layers of 500 turns each. If the magnitude of magnetic field inside the solenoid near its centre is $4.4 \mathrm{mT}$, the current carried is
  1. $1.4 \mathrm{~A}$
  2. $1.5 \mathrm{~A}$
  3. $1.6 \mathrm{~A}$
  4. $1.8 \mathrm{~A}$

Solution

We have $\begin{aligned} & \mathrm{B}=\mu_0 \mathrm{nI} \\ & 4.4 \times 10^{-3}=\mu_0 \frac{\mathrm{N}}{1} \mathrm{I} \\ & 4.4 \times 10^{-3}=4 \pi \times 10^{-7} \times \frac{2500}{1} \times \mathrm{I} \\ & \quad[\because \mathrm{N}=500 \times 5=2500]\end{aligned}$ $\Rightarrow \quad \mathrm{I}=1.4 \mathrm{~A}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

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