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.

Answer 1

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, \(B = \frac{μ_0NI}{l}\)
Where, \(μ_0\) = Permeability of free space = \(4π \times 10^7 \,TmA^{-1}\)
                         \( B = \frac{4π \times10^{-7} \times 2000  \times  8}{0.8}\)
                            \(= 2.5 \times 10^{-2} T\)
Hence, the magnitude of the magnetic field inside the solenoid near its centre is \(2.5 \times 10^{-2} T\).