Question

Rate of change of torque $t$ with deflection $\theta$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$, when

• A. $\theta =0^{\circ }$
• B. $\theta =45^{\circ }$
• C. $\theta =60^{\circ }$
• D. $\theta =90^{\circ }$

Answer 1

Answer: (A)

Torque acting on a bar magnet suspended - magnetic field of induction $B$ is
$\tau =MB\sin \theta$
On differentiation we get
$\frac{d\tau }{d\theta }=MB\cos \theta$
$\therefore$ Rate of change of torque
$\Rightarrow \frac{dz}{d\theta }=MB\cos \theta$ Obviously,
for maximum value of $\frac{d\tau }{d\theta }$
$\cos \theta =1$ or $\theta =0^{\circ }$