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 $2.5 \times 10^{-2} T$.