Question : 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.
Doubt by Nevaeh
Solution :
In all such questions, length of the wire will be same as the same coil is unwound and rewound.
R1 = R
R2 = R/2 (Given)
R1/R2 = 2 — (1)
Length of the wire = N1 × 2πR = N2 × 2π (R/2)
N1 = N2/2
N1/N2 = 1/2 — (2)
Now, The ratio of magnetic moments :
M1/M2 = N1IA1/N2IA2
M1/M2 = N1A1/N2A2
= N1×πR1/N2×πR2
= (N1/N2)×(R1/R2)2
= 1/2 × (2)2
= 2
M1 : M2 = 2 : 1
Similar Question : A circular coil of N turns and diameter d carries a current I. It is unwounded 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.
Ans : M1 : M2 = 1 : 2
Similar Question : A circular coil of N turns and diameter d carries a current I. It is unwounded 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.
Ans : M1 : M2 = 1 : 2