The electric current in a circular coil of 2 turns produces a magnetic induction B₁ at its centre. The coil is unwound and is rewound into  circular coil of 5 turns and at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B₂ at its centre. The ratio of $\frac{B_2}{B_1}$  is

<p><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>l</mi></mrow><mrow><mn>2</mn><mi>R</mi></mrow></mfrac></mrow></math>&nbsp;given N1 = 2</p><p>When new loop is made the length of wire remains same, so</p><p><math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><mn>2</mn><mi>π</mi><mi>r</mi><mo>=</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><mn>2</mn><mi>π</mi><mi>R</mi><mo>⇒</mo><mi>r</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>R</mi></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mfrac><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>=</mo><msup><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>2</mn><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></p>

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