A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each.

Solution:

Length of the solenoid, L = 60 cm = 0.6 m

Radius of the solenoid, r = 4.0 cm = 0.04 m

It is given that there are 3 layers of windings of 300 turns each.

$\therefore$ Total number of turns, $n=3 \times 300=900$

Length of the wire, l = 2 cm = 0.02 m

Mass of the wire, m = 2.5 g = 2.5 × 10−3 kg

Current flowing through the wire, i = 6 A

Acceleration due to gravity, g = 9.8 m/s2

Magnetic field produced inside the solenoid, $B=\frac{\mu_{0} n I}{L}$

Where,

$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$

I = Current flowing through the windings of the solenoid

Magnetic force is given by the relation,

$F=B i l$

$=\frac{\mu_{0} n I}{L} i l$

Also, the force on the wire is equal to the weight of the wire.

$\therefore m g=\frac{\mu_{0} n \text { Iil }}{L}$

$I=\frac{m \mathrm{~g} L}{\mu_{0} n i l}$

$=\frac{2.5 \times 10^{-3} \times 9.8 \times 0.6}{4 \pi \times 10^{-7} \times 900 \times 0.02 \times 6}=108 \mathrm{~A}$

Hence, the current flowing through the solenoid is 108 A.