JEE MAIN - Physics (2022 - 25th July Evening Shift - No. 1)
The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The ratio of $${{{B_2}} \over {{B_1}}}$$ is
$${5 \over 2}$$
$${25 \over 4}$$
$${5 \over 4}$$
$${25 \over 2}$$
Explanation
$$B = {{n{\mu _0}I} \over {2R}}$$
$${B_1} = {{2{\mu _0}I} \over {2{R_1}}}$$
$${B_2} = {{5{\mu _0}I} \over {2{R_2}}}$$
$${R_2} = {{2{R_1}} \over 5}$$
$$ \Rightarrow {{{B_2}} \over {{B_1}}} = {5 \over 2} \times {{{R_1}} \over {{R_2}}} = {{25} \over 4}$$
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