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 π R^2

\;\text " After rewinding, "\; \;\; 2 π R\;=4 a

∴ \;a\;=\;{π R}/{2}

{\M}_{\;\text "square "\;}\;=N I a^2

Or,

\; {\M}_{\;\text "square "\;}\;=N I (\;{π R}/{2}) ^2

∴ {\M}_{\;\text "square "\;}\;=\;{N I π^2 R^2}/{4}

Now,

\; {\M}_{\;\text "square "\;}\;=\;{π}/{4}

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