Question

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 1

We know, 

Magnetic moment (m) = NIA 

Where N = Number of turns

Then, length of wire remains same

Now, m_A = NIA_A = NI (πr²_A) = \(\frac{1}{2}\)NIπd²

Similarly m_B = N'I A_B = \(\frac{NI}{2}\) (πr²_B) = \(\frac{1}{2}\)(NIπd²)