Given:

Length of solenoid, L₁ = 60 cm

Radius of solenoid, r = 4 cm

Number of layers, n₁ = 3

Number of turns, N = 300

Total number of turns,n = N × n₁ = 900

Length of wire, L₂ = 2 cm

Mass of wire, m = 2.5 gm

Current flowing through the wire, I₂ = 6 A

Acceleration due to gravity, g = 9.8 ms^-2

Intuitively, this problem can be broken down into three parts. In first part we will establish the magnetic field inside the solenoid and in second part we introduce a current carrying conductor in the magnetic field. Then we can evaluate the force on the wire. In the final part we try to find the balancing force and finally the current.

Part (1)

We know that magnetic field inside a solenoid is given by,

…(1)

Where,

B = Magnetic field strength

n = total number of turns

I₁ = current through the coil

L₁ = length of the coil

�₀ is the permeability of free space.

�₀ = 4 × π × 10^-7 TmA^-1

Part (2)

We know that, when a current carrying conductor is placed in a magnetic field, it experiences a force given by,

F = B × I₂ × L₂ …(2)

Now putting the value of B from equation 1 into equation 2.

…(3)

Where, I₂ = current through the conductor

L₂ = length of wire

Part (3)

Since, the wire is suspended inside the solenoid, the upward force on it must be equal to its weight.

By equating the weight (m × g) of the body with force in equation (3), we get

m × g = …(4)

⇒ I₁ =

⇒ I₁ =

Note: It can be noted that in SI base units Tesla(T) = Kgs^-2A^-1

⇒ I₁ = 108A

Hence the current flowing through the solenoid is 108A.

for the suspension of the wire.