JEE Advanced 2021 Paper 2 Q13 Physics Electrostatics & Circuits EM Induction Medium

JEE Advanced 2021 Paper 2 · Q13 · EM Induction

When the dipole $m$ is placed at a distance $r$ from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

  1. A. $m/r^3$
  2. B. $m^2/r^2$
  3. C. $m/r^2$
  4. D. $m^2/r$
Reveal answer + step-by-step solution

Correct answer:A

Solution

The superconducting loop maintains zero net flux through itself (initial flux was zero). Total flux $= $ flux from external dipole through loop plus flux from induced current's own dipole moment. To good approximation, equating fields at the loop centre: external dipole field on axis at distance $r$ is $\mu_0 m/(2\pi r^3)$. Induced current $i_1$ in loop of radius $a$ produces field at its own centre $\mu_0 i_1/(2a)$. Setting the two equal (zero-flux condition for $r \gg a$): $\mu_0 m/(2\pi r^3) = \mu_0 i_1/(2a)$, giving $i_1 = m a/(\pi r^3) \propto m/r^3$.

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