In the figure, there is a conducting wire having current i and which has a shape of closed half ellipse $[\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1]$ is kept in a uniform magnetic field B as shown. The magnitude of magnetic dipole moment of loop and torque acting on it are-

Option 1 -

π abi,0

Option 2 -

π a bi, p abiB

Option 3 -

$\frac{π a b i}{2}, \frac{π a b i B}{2}$

Option 4 -

$\frac{π a b i}{2}, 0$

7 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

Area of ellipse = $π a b$

Magnetic dipole moment = $\frac{π a b i}{2}$

Torque $\vec{τ} = \vec{M} \times \vec{B}$

$τ = M B s i n θ$

$? \vec{M} | | \vec{B}$ $τ = 0$

Area of ellipse =  <math> <mrow> <mi>π</mi> <mi>a</mi> <mi>b</mi> </mrow> </math> Magnetic dipole moment = <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1819012439"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mfrac> <mrow> <mi>π</mi> <mi>a</mi> <mi>b</mi> <mi>i</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> Torque <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1819012440"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mover accent="true"> <mi>τ</mi> <mo>→</mo> </mover> <mo>=</mo> <mover accent="true"> <mi>M</mi> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mi>B</mi> <mo>→</mo> </mover> </mrow> </math>   <math> <mrow> <mi>τ</mi> <mo>=</mo> <mi>M</mi> <mi>B</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>θ</mi> </mrow> </math>         <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1819012441"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mo>? </mo> <mover accent="true"> <mi>M</mi> <mo>→</mo> </mover> <mo>|</mo> <mo>|</mo> <mover accent="true"> <mi>B</mi> <mo>→</mo> </mover> </mrow> </math> <math> <mrow> <menclose notation="box"> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0</mn> </mrow> </menclose> </mrow> </math>           <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1819012442"> </o:OLEObject></xml><! [endif]->   <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1819012443"> </o:OLEObject></xml><! [endif]->

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In the figure, there is a conducting wire having current i and which has a shape of closed half ellipse $[\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1]$ is kept in a uniform magnetic field B as shown. The magnitude of magnetic dipole moment of loop and torque acting on it are-

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In the figure, there is a conducting wire having current i and which has a shape of closed half ellipse [ x 2 a 2 + y 2 b 2 = 1 ] is kept in a uniform magnetic field B as shown. The magnitude of magnetic dipole moment of loop and torque acting on it are-

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In the figure, there is a conducting wire having current i and which has a shape of closed half ellipse $[\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1]$ is kept in a uniform magnetic field B as shown. The magnitude of magnetic dipole moment of loop and torque acting on it are-