A coil of ' N ' turns and radius ' R ' ...

CBSE Class 12 Physics 2013 Paper

Question : 10 of 29

Marks: +1, -0

A coil of '

N

' turns and radius '

R

' carries a current '

T

. It is unwound and rewound to make a square coil of side 'a' having same number of turns

(N)

. Keeping the current 'T same, find the ratio of the magnetic moments of the square coil and the circular coil.

Solution:

\text{Magnetic moment} = M = N I A

M_{\text{circular}} = N I \pi R^2

\text{After rewinding,} 2 \pi R = 4 a

\therefore a = \frac{\pi R}{2}

M_{\text{square}} = N I a^2

Or,

M_{\text{square}} = N I \left( \frac{\pi R}{2} \right)^2

\therefore M_{\text{square}} = \frac{N I \pi^2 R^2}{4}

Now,

M_{\text{square}} = \frac{\pi}{4}

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