Two magnets A and B are identical and these are arranged as shown in fig.
Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point p which gets deflected through al angle $θ$ under the influence of magnets. The ratio of distances d₁ and d₂ will be

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$(2 \tan θ)^{- 1 / 3}$

$(2 \cot θ)^{- 1 / 3}$

$(2 \cot θ)^{1 / 3}$

${(2tan⁡θ)}^{1 / 3}$

answer is C.

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Detailed Solution

Applying tangent law, we get
$\begin{array}{l} B_{A} = B_{B} \tan θ \\ \frac{μ_{0}}{4 π} (\frac{2 M}{d_{1}^{3}}) = \frac{μ_{0}}{4 π} (\frac{M}{d_{2}^{3}}) \tan θ \\ ∴ \frac{d_{1}}{d_{2}} = (2 \cot θ)^{1 / 3} \end{array}$

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