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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.

Solution
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Length of solenoid L=80cm=0.8m
Diameter of solenoid d=1.8cm
As d<<L, thus we can treat the solenoid as solenoid of infinite length w.r.t its diameter.
Current flowing through the solenoid I=8.0 A
Total number of turns N=5×400=2000 turns
Number of turns per unit length n=NL
n=20000.8=2500
Magnetic field at the center of solenoid B=μonI
B=4π×107×2500×8.0
We get B=2.5×102 T

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