Question

A circular coil of N turns and radius R carriers 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 original coil.​

Answer 1

Answer:

Explanation:

Magnetic moment of current loop, M =NIA

For circular loop Mc = NI∏R^2

When the coil is unwound and rewound to make a square coil, then 2∏R =4a

a = ∏R/2

Hence, Magnetic moment of square coil Ms = NIa^2

= NI〖 ((∏R)/2)〗^2

= (NI∏^2 R^2)/4

Now, ratio of magnetic moments of the square coil and circular coil

Ms/ Mc = (NI∏^2 R^2)/4/ NI∏R^2

= ∏/4

Answer 2

Answer:

We have,

N1 . 2πR = N2 . 2π(R/2)

.°. N2 = N1

Magnetic Moment of a coil M = NAI

For the coil of radius 'R'

M1 = N1*I*A1 = N1*I*πR^2

For the coil of radius R/2

M2 = N2*I*A2 = 2N1*I*π(R^2/4)

M2 = N1*πR^2/2

=> M2 : M1 = 1 : 2

OR

=> M1 : M2 = 2 : 1

⭕ Hope it helps ⭕