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A solenoid of 1.5 m long with inner diameter of 4 cm has three layers of windings of 1000 turns each & carries a current of 2 A. The magnetic flux through a cross section of the solenoid is nearly.....

(a) 2.5 × 10–7wb 

(b) 6.31 × 10–6wb 

(c) 2.1 × 10–6wb 

(d) 4.1 × 10–5wb

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The correct option (b) 6.31 × 10–6 wb

Explanation:

L = 1.5 m

I = 2A

Total number of turns = 3 × 1000 = 3000

∴ Turns per unit meter = n = [(3000) / (1.5)] = 2000

r = [(4 cm)/2] = 2 × 10–2 m

As   ɸ = AB cos θ = AB cos 0

ɸ = AB

put B = μonI & A = πr2 we get

ɸ = π r2 × μonI = π × (2 × 10–2)2 × 4π × 10–7 × 2000 × 2

∴   θ = 6.31 × 10–6wb 

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