Question

draw the orientation of electric dipole moment un a uniform field such that dipole experience 1/roit 2 times the maximum torque​

Answer 1

To draw:

Orientation of an short electric dipole in a uniform electrostatic field such that the dipole experiences a torque equal to 1/√2 times the max torque.

Concept:

Torque of dipole is calculated as:

$| \tau| = P \times E \times \sin( \theta)$

where , P is the dipole moment , E is the Field Intensity and $\theta$ is the angle between the dipole moment and the field intensity.

Max torque is seen for 90° angle :

$| \tau| = P \times E \times \sin( 90 \degree)$

$= > | \tau| = P \times E \times 1$

$= > | \tau| = PE$

Now , dipole is oriented in such a way that it experiences 1/√2 times of max torque :

$| \tau| = P E \sin( \theta) = \dfrac{1}{ \sqrt{2} } \bigg \{PE \bigg \}$

$= > \sin( \theta) = \dfrac{1}{ \sqrt{2} }$

$= > \theta = 45 \degree \: or \: 135 \degree$

Refer to the attached diagram.