JEE Advanced 2021 Paper 2 Q14 Physics Electrostatics & Circuits EM Induction Medium

JEE Advanced 2021 Paper 2 · Q14 · EM Induction

The work done in bringing the dipole from infinity to a distance $r$ from the center of the loop by the given process is proportional to

  1. A. $m/r^5$
  2. B. $m^2/r^5$
  3. C. $m^2/r^6$
  4. D. $m^2/r^7$
Reveal answer + step-by-step solution

Correct answer:C

Solution

Induced dipole moment of the loop: $m_1 = i_1 \cdot \pi a^2 \propto m a^3/r^3$ from Q.13. Force between the two facing-north dipoles (repulsive): $F = k\, m\, m_1 / r^4 \propto m \cdot (m a^3/r^3)/r^4 = m^2 a^3/r^7$. Work to bring from $\infty$ to $r$ against this repulsive force: $W = \int_\infty^r F\,(-dr')$ in magnitude $= \int_r^\infty F\,dr' \propto m^2 \int_r^\infty dr'/r'^7 \propto m^2/r^6$. Hence $W \propto m^2/r^6$.

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