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JEE Advanced 2021Paper 2
Exam
JEE Advanced
Year
2021
Paper
Paper 2
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Advanced 2021 · Paper 2 · Physics · Magnetic Effects of Current

Two concentric circular loops, one of radius R and the other of...

Two concentric circular loops, one of radius RR and the other of radius 2R2R, lie in the xyxy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1{I}_{1} in the anti-clockwise direction and the larger loop carries current I2{I}_{2} in the clockwise direction, with I2>2I1.B→(x,y)denotesthemagneticfieldatapoint(x,y)inthe{I}_{2} > 2{I}_{1} . \overset{\to}{B}\left(x, y\right) denotes the magnetic field at a point \left(x, y\right) in thexy−plane.Whichofthefollowingstatement(s)is(are)correct?</p><p><imgsrc="https://cdn−question−pool.getmarks.app/pyq/jeeadvanced/943fc473−a8ae−4dd6−b9e0−694ca23ed9f2−image.png"style="width:230px;height:213px;"/></p>-plane. Which of the following statement(s) is (are) correct?</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/943fc473-a8ae-4dd6-b9e0-694ca23ed9f2-image.png" style="width: 230px; height: 213px;" /> </p>

Options

  1. A\overset{\to}{B}(x,y)\left(x, y\right) is perpendicular to the xyxy-plane at any point in the plane
  2. B\left|\overset{\to}{B}\left(x, y\right)\right| depends on xx and yy only through the radial distance r=x2+y2r = \sqrt{{x}^{2} + {y}^{2}}
  3. C\left|\overset{\to}{B}\left(x, y\right)\right|isnon−zeroatallpointsforis non-zero at all points forr < R
  4. DB→\overset{\to}{B}\left(x, y\right)pointsnormallyoutwardfromthepoints normally outward from thexy-plane for all the points between the two loops

Correct answer

A. \overset{\to}{B}(x,y)\left(x, y\right) is perpendicular to the xyxy-plane at any point in the plane

Step-by-step solution

Two concentric circular loops, one of radius R and the other of radius 2R , lie in the xy -plane with the origin as (A) Magnetic field at the plane of the ring is perpendicular to the plane. However, they bend as they move forward. Two concentric circular loops, one of radius R and the other of radius 2R , lie in the xy -plane with the origin as (B) By symmetry, we can say thatB→\overset{\to}{B}will be same at all the points having the same radial distance. soB→\overset{\to}{B}(x,y)\left(x, y\right)will depend only the radial distancer=x2+y2r = \sqrt{{x}^{2} + {y}^{2}} Two concentric circular loops, one of radius R and the other of radius 2R , lie in the xy -plane with the origin as (C)(B net ){\left({B}_{\text{ net }}\right)}_{centre} = \dfrac{{\mu}_{0}{I}_{2}}{2\left(2R\right)} - \dfrac{{\mu}_{0}{I}_{1}}{2R} = \dfrac{{\mu}_{0}}{4R}\left({I}_{2} - 2{I}_{1}\right)Since,I2>2I1{I}_{2} > 2{I}_{1}soBnet{B}_{net}at the centre will be non-zero in⊗⊗direction, But at some other point,Bnet{B}_{net}may be zero. From the graph, it is clear thatBnet=0{B}_{net} = 0for some value ofr∈(0,R)r \in \left(0, R\right). Sooption (C) is incorrect Two concentric circular loops, one of radius R and the other of radius 2R , lie in the xy -plane with the origin as Two concentric circular loops, one of radius R and the other of radius 2R , lie in the xy -plane with the origin as (D) For the graph, it is clear thatB=−ve⇒B = - ve ⇒in⊗⊗direction forr∈(Rto2R)r \in \left(Rto2R\right), so option D is also incorrect.
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