The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph the variation of different quantities with distance.

 

Correct Option - 1


Detailed Solution:

When arm PQ of a rectangular conductor is moving from x = 0 to x = b, the flux $\left(?=ax\right)$ linked with loop increases and while moving from x = b to x = 2b and from x = 2b to x = b, $\left(?=ab\right)$ flux remains constant and then flux $\left(?=ax\right)$ decreases to zero as it moves from x = b to x = 0.

$e_{in}=-\frac{d?}{dt}=-a\frac{dx}{dt}=-av\Rightarrow$ Induced emf

$P=\frac{{\left(e_{in}\right)}^2}{R}\Rightarrow$ Power dissipated

 

<p>When arm PQ of a rectangular conductor is moving from x = 0 to x = b, the flux <span contenteditable="false"> <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>? </mi> <mo>=</mo> <mi>a</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816091991"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;linked with loop increases and while moving from x = b to x = 2b and from x = 2b to x = b, <span contenteditable="false"> <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>? </mi> <mo>=</mo> <mi>a</mi> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>flux &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816091992"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;remains constant and then flux <span contenteditable="false"> <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>? </mi> <mo>=</mo> <mi>a</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1816091993"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;decreases to zero as it moves from x = b to x = 0.</p><p><span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mfrac> <mrow> <mi>d</mi> <mi>? </mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>−</mo> <mi>a</mi> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>−</mo> <mi>a</mi> <mi>v</mi> <mo>⇒</mo> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1816091994"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;Induced emf</p><p><span contenteditable="false"> <math> <mrow> <mi>P</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>⇒</mo> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1816091995"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;Power dissipated</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754566646php75NriH.jpeg" alt="" width="292" height="168" loading="lazy"></picture></div></div><p>&nbsp;</p>

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