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QJEEM24Ph6dc5: JEE Main 2024 Physics - Class 12 JEEM24Ph6dc5 Solution: A coil of 200 turns and area is rotated at half a revolution…

A coil of 200 turns and area 0.20 m20.20 \mathrm{~m}^2 is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T0.01 \mathrm{~T} perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is 2πβ\frac{2 \pi}{\beta} volt. The value of β\beta is _______.

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padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd extra="true"></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em;"><mjx-mi class="mjx-n"></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mfrac space="4"><mjx-frac type="d"><mjx-num><mjx-nstrut type="d"></mjx-nstrut><mjx-mrow><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi></mjx-mrow></mjx-num><mjx-dbox><mjx-dtable><mjx-line type="d"></mjx-line><mjx-row><mjx-den><mjx-dstrut type="d"></mjx-dstrut><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mfrac space="4"><mjx-frac type="d"><mjx-num><mjx-nstrut type="d"></mjx-nstrut><mjx-mrow><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi></mjx-mrow></mjx-num><mjx-dbox><mjx-dtable><mjx-line type="d"></mjx-line><mjx-row><mjx-den><mjx-dstrut type="d"></mjx-dstrut><mjx-mn class="mjx-n"><mjx-c class="mjx-c35"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac><mjx-texatom texclass="ORD"><mjx-mi class="mjx-n"><mjx-c class="mjx-c76"></mjx-c><mjx-c class="mjx-c6F"></mjx-c><mjx-c class="mjx-c6C"></mjx-c><mjx-c class="mjx-c74"></mjx-c></mjx-mi></mjx-texatom><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-table></mjx-mtable></mjx-math><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>ϕ</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">NAB</mi></mrow><mi>cos</mi><mo data-mjx-texclass="NONE">⁡</mo><mo stretchy="false">(</mo><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi>ε</mi><mo>=</mo><mo>−</mo><mfrac><mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><mi>ϕ</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">dt</mi></mrow></mfrac><mo>=</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">NAB</mi></mrow><mi>ω</mi><mi>sin</mi><mo data-mjx-texclass="NONE">⁡</mo><mo stretchy="false">(</mo><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OP" movablelimits="true">max</mo></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">NAB</mi></mrow><mi>ω</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>200</mn><mo>×</mo><mn>0.2</mn><mo>×</mo><mn>0.01</mn><mo>×</mo><mi>π</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mn>10</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mn>5</mn></mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">volt</mi></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>

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