JEE Advanced 2021 Paper 2 Q06 Physics Magnetism Magnetic Field Medium

JEE Advanced 2021 Paper 2 · Q06 · Magnetic Field

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 centre, 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 $I_2 > 2 I_1$. $\vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $xy$-plane. Which of the following statement(s) is(are) correct?

[Figure: Two concentric circles of radii R and 2R centred at origin in xy-plane. Inner loop with current I1 (anticlockwise), outer with I2 (clockwise).]

  1. A. $\vec{B}(x, y)$ is perpendicular to the $xy$-plane at any point in the plane
  2. B. $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r = \sqrt{x^2 + y^2}$
  3. C. $|\vec{B}(x, y)|$ is non-zero at all points for $r < R$
  4. D. $\vec{B}(x, y)$ points normally outward from the $xy$-plane for all the points between the two loops
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:A, B

Solution

By symmetry of the two coaxial circular loops, at any point in the $xy$-plane the magnetic field has no in-plane component (in-plane components from diametrically opposite current elements cancel). Hence $\vec{B}$ is perpendicular to the $xy$-plane — (A) correct. By rotational symmetry about the $z$-axis, $|\vec{B}|$ depends only on $r = \sqrt{x^2+y^2}$ — (B) correct. At the centre, $B = \mu_0 I_1/(2R) - \mu_0 I_2/(2\cdot 2R) = \mu_0(2I_1 - I_2)/(4R) < 0$ since $I_2 > 2I_1$, so $B$ at centre is non-zero but the field can vanish at some $r < R$ because the contributions oppose and vary differently — there exist points inside the inner loop where $B = 0$, so (C) is wrong. The field direction reverses between the loops (closer to either loop the corresponding loop dominates), so (D) is wrong.

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