A magnetized wire of magnetic moment M is bent into an are of a circle that subtends an angle of 30° at the centre. The equivalent magnetic moment is found to be Q times M. The numerical value of M should be _____

Answer

`01.90`

Explanation

Let r be the radius of the circle. The length of the arc

`=2pir xx 30^(@)/360^(@)`
`= (pir)/6`…….. (i)
Length of magnetized wire .... (ii)
From (i) and (ii)
`2l = (pir)/6 rArr r = (12l)/pi`
If m is the pole strength of each pole of the magnet, the magnetic moment of the arc
`M. = m xx r`
`= m xx ((12l)/pi)`
`= (6 xx (2ml))/pi = 6/pi M`............... `[therefore M = 2ml]`
`therefore M. = 1.9 M`