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(A) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by the formula:$	au = p E \sin 	heta$ ...$(i)$where $p$

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$(a)$

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(A) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by the formula:$	au = p E \sin 	heta$ ...$(i)$where $p$ is the electric dipole moment and $	heta$ is the angle between the dipole moment vector and the electric field direction.Analyzing the torque at different angles:$1$. At $	heta = 0^{\circ}$,$	au = p E \sin 0^{\circ} = 0$.$2$. At $	heta = \frac{\pi}{2}$,$	au = p E \sin \frac{\pi}{2} = p E$.$3$. At $	heta = \pi$,$	au = p E \sin \pi = 0$.$4$. At $	heta = \frac{3\pi}{2}$,$	au = p E \sin \frac{3\pi}{2} = -p E$.$5$. At $	heta = 2\pi$,$	au = p E \sin 2\pi = 0$.This variation follows a sine wave pattern starting from zero,reaching a maximum at $\frac{\pi}{2}$,passing through zero at $\pi$,reaching a minimum at $\frac{3\pi}{2}$,and returning to zero at $2\pi$. The graph representing this behavior is the standard sine curve.

Column-$I$ (Angle between $\vec{p}$ and $\vec{E}$)	Column-$II$ (Potential energy of the dipole)
$a. 180^{\circ}$	$i. -pE$
$b. 120^{\circ}$	$ii. pE$
$c. 90^{\circ}$	$iii. \frac{1}{2} pE$
	$iv. 0$

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