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
$\tau=M B \sin \theta$
On differentiation we get
$\frac{d \tau}{d \theta}=M B \cos \theta$
$\therefore $ Rate of change of torque
$\Rightarrow \frac{d z}{d \theta}=M B \cos \theta$ Obviously,
for maximum value of $\frac{d \tau}{d \theta}$
$\cos \theta=1$ or $\theta=0^{\circ}$