Question

3.A circular coil of n turns and radius r carries a current i. It is unwound and rewound to make another coil of radius r/2, current i remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. [all india 2012]

Answer 1

Answer:

1/2

Explanation:

B1=uni/2r

B2=uni/(2×r/2)

B2/B1=r/2r=1/2

Answer 2

Answer:

Area of the coil initially A=πR

2

∴ Initial magnetic moment μ=NIA=NI(πR

2

)

Length of the coil initially L=N(2πR)

Radius of new coil formed R

′

=

2

R

Let the number of turns in new coil be N

′

.

But the length of the new coil formed must be equal to that of original coil i.e L

′

=L

∴ N

′

×2π

2

R

=N×2πR ⟹N

′

=2N

Thus area of new coil A

′

=

4

πR

2

∴ Magnetic moment of new coil μ

′

=N

′

IA

′

=2NI×

4

πR

2

=

2

NIπR

2

$= \frac{1}{2}$