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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
Length of the solenoid, l = 80 cm = 0.8 m
There are five layers of windings of 400 turns each on the solenoid.
∴ Total number of turns on the solenoid, N = 5 × 400 = 2000
Diameter of the solenoid, D = 1.8 cm = 0.018 m
Current carried by the solenoid, I = 8.0 A
Magnitude of the magnetic field inside the solenoid near its centre is given by the relation,
B = `(mu_0"NI")/"l"`
Where,
`mu_0` = Permeability of free space
= 4π × 10–7 T m A–1
B = `(4pi xx 10^-7 xx 2000 xx 8)/(0.8)`
= 8π × 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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