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Physics-

General

Easy

Question

Two magnets A and B are identical and these are arranged as shown in the figure. 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 an angle $theta$ under the influence of magnets. The ratio of distance $d subscript 1 end subscript$ and $d subscript 2 end subscript$ will be

$(2 \tan θ)^{1 / 3}$
$(2 \tan θ)^{- 1 / 3}$
$(2 \cot θ)^{1 / 3}$
$(2 \cot θ)^{- 1 / 3}$

The correct answer is: $left parenthesis 2 cot invisible function application theta right parenthesis to the power of 1 divided by 3 end exponent$

In equilibrium $B subscript 1 end subscript equals B subscript 2 end subscript tan invisible function application theta$

$rightwards double arrow fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator 2 M over denominator d subscript 1 end subscript superscript 3 end superscript end fraction equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator M over denominator d subscript 2 end subscript superscript 3 end superscript end fraction tan invisible function application theta$
$rightwards double arrow fraction numerator d subscript 1 end subscript over denominator d subscript 2 end subscript end fraction equals open parentheses 2 cot invisible function application theta close parentheses to the power of 1 divided by 3 end exponent$

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