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Torques $τ_{1}$ and $τ_{2}$ are required for a magnetic needle to remain perpendicular to the magnetic fields B₁ and B₂ at two different places. The ratio of B₁ / B₂ is

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$\frac{τ_{2}}{τ_{1}}$

$\frac{τ_{1}}{τ_{2}}$

$\frac{τ_{1} + τ_{2}}{τ_{1} - τ_{2}}$

$\frac{τ_{1} - τ_{2}}{τ_{1} + τ_{2}}$

answer is B.

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Detailed Solution

Torque, $τ = M B \sin θ$

$∴ τ_{1} = M B_{1} \sin 90 ° = M B_{1}$

and $τ_{2} = M B_{2} \sin 90 ° = M B_{2} or \frac{M B_{1}}{M B_{2}} = \frac{τ_{1}}{τ_{2}}$

$∴ \frac{B_{1}}{B_{2}} = \frac{τ_{1}}{τ_{2}}$

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