A 60 cm long solenoid of radius `4.0 cm` has 3 layers of windings of 300 turns each. A.2.0 cm long wire of mass 2.5g 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 6.0A in the wire. What value of current (with appropriate sense of circulation) in the windling of the solenoid can support the weight of the wire ? `g=9.8m*s^(-2)`.

Explanation

`F=BIl and =mu_(0)*(N)/(l)*I'`
`:.F=mu_(0)*(N)/(l')I'*I*l` [where, I'= required current, l'= length of the solenoid, I= current from battery, l= length of the wire]
This force will neutralise the gravitational force on the wire.
`:. Mu_(0)N*(l)/(l)*I'*I=mg`
or, `I'=(mgl')/(mu_(0)NlI)`
`=(2.5xx10^(-3)xx9.8xx60xx10^(-2))/(4pi xx10^(-7)xx3xx300xx2.0xx10^(-2)xx6.0)`
`=108.3A`