Question

A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windingsof 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside thesolenoid (near its centre) normal to its axis; both the wire and theaxis of the solenoid are in the horizontal plane. The wire is connectedthrough two leads parallel to the axis of the solenoid to an externalbattery which supplies a current of 6.0 A in the wire. What value ofcurrent (with appropriate sense of circulation) in the windings ofthe solenoid can support the weight of the wire? g = 9.8 m s–2.

Answer 1

Given: The length of the solenoid coil is 60 cm and radius is 4 cm, the solenoid has 3 layers of windings of 300 turns each, the length of the wire is 2.0 cm and mass of the wire is 2.5 g. The current flowing through the wire is 6 A.

The total number of turns is given as,

n=300×3 =900

The formula for the magnetic force acting on the wire is given as,

F=Bil = μ 0 nI L il (1)

Also force under gravitational pull from Newton’s law of motion is given as,

F=mg(2)

On comparing equation (1) and equation (2), we get

mg= μ 0 nI L il I= mgL μ 0 nil

By substituting the given values in above equation, we get

I= 2.5×9.8×0.6 4π× 10 −7 ×900×0.02×6 =108 A

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