A planar loop of wire rotates in a uniform magnetic field. Initially, at <math> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math> , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of <math> <mn>10</mn> <mtext> </mtext> <mi mathvariant="normal">s</mi> </math> about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

At any time t  ? = B A c o s ? π t 5 ? ω = 2 π T = 2 π 10 = π 5  d ? d t = - π 5 B A s i n ? π t 5  e = π 5 B A s i n ? π t 5 e will be maximum when π t 5 is <!-- [if gte msEquation 12]>π2

A planar loop of wire rotates in a uniform magnetic field. Initially, at <math> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math> , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of <math> <mn>10</mn> <mtext> </mtext> <mi mathvariant="normal">s</mi> </math> &nbsp;about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

5.0 and <math> <mn>7.5</mn> <mtext> </mtext> <mi mathvariant="normal">s</mi> </math> <math><mtext></mtext></math>

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Electromagnetic Induction Physics Ncert Solutions Class 12th Physics Class 12th

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

Option 1 -

$2.5 s$ and $5.0 s$

Option 2 -

$5.0 s$ and $10.0 s$

Option 3 -

$2.5 s$ and $7.5 s$

Option 4 -

5.0 and $7.5 s$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

At any time $t$

$? = B A c o s ? \frac{π t}{5} (? ω = \frac{2 π}{T} = \frac{2 π}{10} = \frac{π}{5})$

$\frac{d ?}{d t} = - \frac{π}{5} B A s i n ? (\frac{π t}{5})$

$e = \frac{π}{5} B A s i n ? (\frac{π t}{5})$

e will be maximum when $\frac{π t}{5}$ is $\frac{π}{2}$ .

$t = 2.5 s e c$
e will be minimum when $\frac{π t}{5}$ is $π, 0$

$t = 0,5 s e c$

So, answer will be (1).

At any time  <math> <mi>t</mi> </math>  <math> <mi>?</mi> <mo>=</mo> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> <mo>?</mo> <mfrac> <mrow> <mrow> <mi>π</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mfenced separators="|"> <mrow> <mrow> <mo>?</mo> <mi>ω</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">T</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math>  <math> <mfrac> <mrow> <mrow> <mi mathvariant="normal">d</mi> <mi>?</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>?</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>π</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math>  <math> <mi mathvariant="normal">e</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>?</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>π</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> e will be maximum when <math> <mfrac> <mrow> <mrow> <mi>π</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </math>  is <img src="file:///C:/Users/ALOK~1.SIN/AppData/Local/Temp/msohtmlclip1/01/clip_image012.png" width="7" height="23"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> . <math> <mi mathvariant="normal">t</mi> <mo>=</mo> <mn>2.5</mn> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">c</mi> </math> e will be minimum when <math> <mfrac> <mrow> <mrow> <mi>π</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </math> is <math> <mi>π</mi> <mo>,</mo> <mn>0</mn> </math>  <math> <mi mathvariant="normal">t</mi> <mo>=</mo> <mn>0,5</mn> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">c</mi> </math> So, answer will be (1).

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A planar loop of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

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A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0 , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

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A planar loop of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at: