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Question
A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
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Solution
Given: Length of the solenoid, l = 80 cm = 0.8 m
Diameter of the solenoid, D = 1.8 cm = 0.018 m
Current carried by the solenoid, I = 8.0 A
There are five layers of windings of 400 turns each on the solenoid.
∴ Total number of turns on the solenoid, N = 5 × 400
= 2000
Formula: n = `"number of turns"/"length"`
= `2000/0.8`
= 2500
Magnetic field near the centre of a long solenoid,
B = μ0nI
= 4π × 10–7 × 2500 × 8.0
= 4π × 10–7 × 20000
= 4π × 10–3 × 2
= 8π × 10–3
= 8 × 3.14 × 10–3
= 25.12 × 10–3
= 2.512 × 10–2 T
Hence, the magnitude of the magnetic field inside the solenoid near its centre is 2.512 × 10–2 T.
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