A circular coil of N turns and diameter d carries a current I . It is unwound and rewound to make another coil of diameter 2d , current I remaining the same . Calculate the ratio of the magnetic moments of the new coil and the original coil .

Answer

2

Explanation

For the original coil , magnetic moment ,
`p_(1)=NIA=NI.(pid^(2))/(4)`
For the new coil , diameter becomes 2d , i. e ., the circumference is doubled . So the number of turns becomes `(N)/(2)` Magnetic moment ,
`p_(2)=(NI)/(2).(pi(2d)^(2))/(4)=NI.(pid^(2))/(4).2=2p_(1)`
`therefore(p_(2))/(p_(1))=(2)/(1)`