JEE Advanced
Physics
Magnetic Effects of Current
2021
JEE Advanced 2021 (Paper 2)
JEE Advanced Physics Question (2021) — Solution
Question
Two concentric circular loops, one of radius R and the other of radius 2 R , lie in the x y -plane with the origin as their common center, as shown in the figure. The smaller loop carries current I 1 in the anti-clockwise direction and the larger loop carries current I 2 in the clockwise direction, with I 2 > 2 I 1 .   B → x , y denotes the magnetic field at a point x , y in the x y -plane. Which of the following statement(s) is (are) correct?
Options
- A. B → x , y is perpendicular to the x y -plane at any point in the plane
- B. B → x , y depends on x and y only through the radial distance r = x 2 + y 2
- C. B → x , y is non-zero at all points for r < R
- D. B → x , y points normally outward from the x y -plane for all the points between the two loops
Answer
B. B → x , y depends on x and y only through the radial distance r = x 2 + y 2
Step-by-step solution
(A) Magnetic field at the plane of the ring is perpendicular to the plane. However, they bend as they move forward. (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 only the radial distance r = x 2 + y 2 (C) B net   centre   = μ 0 I 2 2 2 R - μ 0 I 1 2 R = μ 0 4 R I 2 - 2 I 1 Since, I 2 > 2 I 1 so B net at the centre will be non-zero in ⊗ direction, But at some other point, B net may be zero. From the graph, it is clear that B net = 0 for some value of r ∈ 0 , R . Sooption (C) is incorrect (D) For the graph, it is clear that B = - v e ⇒ in ⊗ direction for r ∈ R   to   2 R , so option D is also incorrect.
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