Question

Torques ${\tau }_1$ and ${\tau }_2$ are required for a magnetic needle to remain perpendicular to the magnetic fields at two different places. The magnetic fields at those places are $B_1$ and $B_2$ respectively; then ratio $\frac{B_1}{B_2}$ is

• A. $\frac{{\tau }_2}{{\tau }_1}$
• B. $\frac{{\tau }_1}{{\tau }_2}$
• C. $\frac{{\tau }_1+{\tau }_2}{{\tau }_1-{\tau }_2}$
• D. $\frac{{\tau }_1-{\tau }_2}{{\tau }_1+{\tau }_2}$

Answer 1

Answer: (B)

$\frac{{\tau }_1}{{\tau }_2}$

$\tau =\overline{M}\times \overline{B}.$ since perpendicular, $\theta ={90}^{\circ }$

${\tau }_1:{\tau }_2$ = $M.B_1.sin{90}^{\circ }$:$M.B_2.sin{90}^{\circ }$=$B_1:B_2$