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A coil carrying current l has radius r...

A coil carrying current l has radius r and number of turns n it is rewound so that radis of new coil is `(r )/(4)` and it carries current l the ratio fo magenic moment of new coil to that of original coil is

A

1

B

`1/2`

C

`1/4`

D

`1/8`

Text Solution

Verified by Experts

The correct Answer is:
b
Magnetic moment of the original coil
`M_(0)=n _(1)IA=nI(pir^(2))`
magnetic mometnt of the new coil
`M_(n)=n_(2)IA=n_(2)I(pi(r^(2))/(16))`
Equating length of the wires we have
`n_(1)xx2pir_(1)=n_(2)xxx2pr_(2)`
`rarr n xx 2pir=n_(2)xx2pixx(r )/(4)`
`rarr n_(2)=4n`
now from eqs (i) and (ii) we get
`(M_(0))/(M_(n))=(n)/(n_(2))xx16=1/4xx16=4`
`rarr (M_(n))/(M_(0))=1/4`
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