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QJEEAdv21Ph5ef2: JEE Advanced 2021 Physics - Class 12 JEEAdv21Ph5ef2 Solution: Two concentric circular loops, one of radius R and the other of …

Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. B→\overrightarrow B (x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

JEE Advanced 2021 Paper 2 Online Physics - Magnetism Question 29 English

Multiple Choice Options

  • A B→\overrightarrow B (x, y) is perpendicular to the xy-plane at any point in the plane
  • B | B→\overrightarrow B (x, y) | depends on x and y only through the radial distance r=x2+y2r = \sqrt {{x^2} + {y^2}}
  • C | B→\overrightarrow B (x, y) | is non-zero at all points for r < R
  • D B→\overrightarrow B (x, y) points normally outward from the xy-plane for all the points between the two loops

Step-by-Step Verified Solution

JEE Advanced 2021 Paper 2 Online Physics - Magnetism Question 29 English Explanation 1
(a) Magnetic field at the plane of the ring is perpendicular to the plane. However, they bend as they move forward.

JEE Advanced 2021 Paper 2 Online Physics - Magnetism Question 29 English Explanation 2
(b) By symmetry, we can say that B will be same at all the points having the same radial distance. So, B (x, y) will depend on the radial distance r=x2+y2r = \sqrt {{x^2} + {y^2}} .

JEE Advanced 2021 Paper 2 Online Physics - Magnetism Question 29 English Explanation 3
(c) (Bnet)centre=μ0I22(2R)−μ0I12R{({B_{net}})_{centre}} = {{{\mu _0}{I_2}} \over {2(2R)}} - {{{\mu _0}{I_1}} \over {2R}}

=μ04R(I2−2I1)= {{{\mu _0}} \over {4R}}({I_2} - 2{I_1}) , since I2 > 2I1, so Bnet at the centre will be non-zero in ⊗\otimes direction. But at some other point, Bnet may be zero.

From the graph, it is clear that Bnet = 0 for r ∈\in (0, R).

So, option (c) is incorrect.

JEE Advanced 2021 Paper 2 Online Physics - Magnetism Question 29 English Explanation 4
(d) For the graph, it is clear that B = −- ve

In, ⊗\otimes direction for r ∈\in (R to 2R), so option (d) is also incorrect.

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