Magnetism and Matter | Physics JEE Main questions with Solutions

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Topic Question Set

Q 1 :

A compass needle oscillates 20 times per minute at a place where the dip is $30 °$ and 30 times per minute where the dip is $60 °$ . The ratio of total magnetic field due to the earth at the two places respectively is $\frac{4}{\sqrt{x}}$ . The value of $x$ is ___________ . [2023]

0%

(243)

$Period of oscillation \propto \frac{1}{\sqrt{B_{H}}}$

$T \propto \frac{1}{\sqrt{B \cos θ}} \Rightarrow \frac{T_{1}}{T_{2}} = \sqrt{\frac{B_{2} \cos θ_{2}}{B_{1} \cos θ_{1}}}$

$\Rightarrow \frac{60 / 20}{60 / 30} = \sqrt{\frac{B_{2} \cos 60 °}{B_{1} \cos 30 °}} \Rightarrow \frac{3}{2} = \sqrt{\frac{B_{2}}{\sqrt{3} B_{1}}}$

$\Rightarrow \frac{9}{4} = \frac{B_{2}}{\sqrt{3} B_{1}} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{4}{9 \sqrt{3}} = \frac{4}{\sqrt{243}}$

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