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

Given : `N=300 times 3=900 turns`
`l=0.60m, m=2.5 times 10^(-3)kg`.
`therefore " "n=N/l=900/0.6`
`" "=1500m^(-1)`
`" "l^(')=2 times 10^(-2)m.`
Magnetic field at the centre of a solenoid `=mu_(0)nI`
Force experienced by the wire `=BI^(')l^(')sin90^(@)`
i.e., `" "F=(mu_(0)nI)I^(')l^(')`
but `F^(')=mg`, where m - mass of the wire
`therefore " "F=F^(')`
`" "mu_(0)nII^(')l^(')=mg`
or `" "I=(mg)/(mu_(0)nI^(')l^('))`
`" "=(2.5 times 10^(-3) times 9.8)/(4 times 3.14 times 10^(-7) times 1500 times 6 times 2 times 10^(-2))`
`" "I=108A`
Hence a current of 108 A can support the weight of the wire.