Question

at what orientation angle relative to the magnetic field direction does the torque on a magnetic dipole have its smallest value? 0° 45° 90° 135° 180°

Explanation:

Step1: Recall torque formula

The torque on a magnetic dipole in a magnetic - field is given by $\tau = \mu B\sin\theta$, where $\mu$ is the magnetic dipole moment, $B$ is the magnetic - field strength, and $\theta$ is the angle between the magnetic dipole moment and the magnetic - field direction.

Step2: Analyze the $\sin\theta$ function

The function $y = \sin\theta$ has values in the range $[- 1,1]$. The magnitude of $\sin\theta$ is minimum when $\sin\theta = 0$.

Step3: Find the angle for minimum $\sin\theta$

$\sin\theta=0$ when $\theta = 0^{\circ}$ or $\theta = 180^{\circ}$. At these angles, the torque $\tau=\mu B\sin\theta = 0$, which is the smallest value of torque.

Answer:

$0^{\circ},180^{\circ}$