A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis, both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire?

Explanation

1.
Magnetic field inside a long current carrying solenoid is B then magnetic force exerted on current carrying wire placed perpendicular to axis of solenoid in the horizontal plane will be,
`F=I.l.Bsin90^(@)`
(Where, I. = current passing through wire)
`thereforeF=I.l.(mu_(0)NI)" "...(1)`
(Where, I = current passing through the windings of solenoid)
2. Direction of above force is vertically upward (see the diagram). If it balances weight of wire then,
F = mg
`thereforeI.l.(mu_(0)nI)=mg`
`therefore(6)(0.02)(4pixx10^(-7)xx(300xx3)/0.6xxI)=(2.5xx10^(-3))(9.8)`
`thereforeI=108.36A`