A closely wound solenoid 80cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8cm. If the current arried is 8.0A, then estimate the magnitude of B inside the solenoid near is centre

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$1.5 \times 10^{- 2} T, along to the axis of solenoid$

$2.5 \times 10^{- 2} T, along the axis of solenoid$

$3.5 \times 10^{- 2} T, along the axis of solenoid$

$1.5 \times 10^{- 2} T, opposite to the axis of solenoid$

answer is B.

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Detailed Solution

The length of solenoid, l = 80cm = 0.8m

The total number of turns, N = 400 × 5 = = 2000 and number of turns / length, $n = \frac{2000}{0 .8} = 2500$

The magnitude of magnetic field inside the solenoid

$B = μ_{0} nl \sin ϕ = 4 \times 3 .14 \times 10^{- 7} \times 2500 \times 8 \times 1 [A s \sin ϕ ≃ 1]$ $= 2.5 \times 10^{- 2} T$

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