A) \[{{\tan }^{-1}}(3)\]
B) \[{{\tan }^{-1}}(2)\]
C) \[{{\tan }^{-1}}(0.5)\]
D) \[{{\tan }^{-1}}(1)\]
Correct Answer: B
Solution :
(b)\[{{\tan }^{-1}}(2)\] Here, \[{{B}_{V}}=\frac{{{\mu }_{0}}}{4\pi }\frac{3m\,\cos \theta }{{{r}^{3}}}\] \[{{B}_{H}}=\frac{{{\mu }_{0}}}{4\pi }\frac{m\,sin\theta }{{{r}^{3}}}\] and \[\delta =45{}^\circ \] \[\because \tan \delta =\frac{{{B}_{V}}}{{{B}_{H}}}\] Hence, \[\tan \,45{}^\circ =\frac{2\cos \theta }{\sin \theta }=2\cot \theta \] \[\therefore 1=\frac{2}{\tan \theta }\Rightarrow \tan \theta =2\] or \[\theta ={{\tan }^{-1}}(2)\] is the loci of points.
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