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The electric current in a circular coil of two turns produced a magnetic induction of 0.25 T at its centre. The coil is unwound and is rewound into a circular coil of four turns. Find the magnetic induction (in T) at the centre of the coil, if same current flows through the coil.

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Detailed Solution

With 2 turns in the coil,

$(2) (2 π r_{1}) = L r_{1} = L / 4 π B_{1} = \frac{μ_{0} N_{1} I}{2 r_{1}} = \frac{2 μ_{0} I}{(2) L / 4 π} = \frac{4 π μ_{0} I}{L}$

With 4 turns in the coil,

$(4) (2 π r_{2}) = L r_{2} = L / 8 π B_{2} = \frac{μ_{0} N_{2} I}{2 r_{2}} = \frac{4 μ_{0} I}{(2) L / 8 π} = \frac{16 μ_{0} I π}{L} \frac{B_{1}}{B_{2}} = \frac{1}{4} B_{2} = 4 B_{1} = (4) (0.25) = 1 T$

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