A circular coil A of 5 turns and radius r carries current l. Another circular coil B of radius 2r and 10 turns
carries current l. The magnetic fields at the centre of the circular coils are in the ratio of M: 1. Find the
value of M.
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Explanation:
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
⟹
μ
μ
′
=
2
1
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