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.

CBSE Class 12 Physics 2013 Paper

Question : 10

Total: 29

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:

‌ Magnetic moment ‌‌=M=NIA
M‌circular ‌‌=NIπR2
‌ After rewinding, ‌‌‌2πR‌=4a
∴‌a‌=‌

πR

M‌square ‌‌=NIa2
Or, ‌M‌square ‌‌=NI(‌

πR

)2
∴M‌square ‌‌=‌

NIπ2R2

Now, ‌M‌square ‌‌=‌

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