A solenoid 60 cm long and of radius 4 cm has 3 layer of windings 300 turns each. A 2.3 cm long wire of mass 2.5g lies inside the solenoide 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 6A 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

To solve the problem step by step, we need to find the current in the solenoid that can support the weight of the wire placed inside it. Let's break down the solution:

### Step 1: Calculate the number of turns per unit length (n) of the solenoid
The solenoid has 3 layers of windings, with each layer having 300 turns. Therefore, the total number of turns \( N \) is:
\[ N = 3 \times 300 = 900 \text{ turns} \]
The length of the solenoid \( L \) is 60 cm, which is equal to:
...