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A coil of N turns and radius R carries I . It is unwound and rewound to make a square coil of side 'a' having same number of turns N. Keeping the curretn I same, find the ratio of the magnetic moments of the square coil and the circular coil. |
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Answer» Solution :Magnetic MOMENT of circular coil of N TURNS and radius R carrying a current I `m_1 = N A_1 I = N pi R^2 I"".........(i) ` When the coil is unwound and is rewound to make another square coil of side .a. and number of turns N, as total LENGTH of wire remains constant , we have `N . 2 pi R = N 4 a implies a= (pi R)/(2)` `:.` Magnetic moment of square coil for SAMECURRENT I `m_2 = NA_2 I = N a^2 I = N ((pi R^2)/(2)) I = N(pi^2 R^2)/(4) I"" .......(ii)` `implies (m_2)/(m_1) = pi/4`. |
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