Question 793: Electrostats & Capacitance

Question

An electric dipole of dipole moment ' $p$ ' is aligned parallel to a uniform electric field ' E '. The energy required to rotate the dipole by $90^{\circ}$ is $\left[\begin{array}{ll}\sin 0^{\circ}=0, & \sin 90^{\circ}=1 \ \cos 0^{\circ}=1, & \cos 90^{\circ}=0\end{array}ight]$

Accepted Answer

Potential energy $(U)$ of an electric dipole in a uniform electric field $E$ at angle $	heta$:
$$ U = -pE \cos	heta $$
Step 1:
Initial position: Dipole is parallel to the field, so $	heta_1 = 0^\circ$.
Initial energy:
$$ U_1 = -pE\cos 0^\circ = -pE 	imes 1 = -pE $$
Step 2:
Final position: Dipole is rotated by $90^\circ$, so $	heta_2 = 90^\circ$.
Final energy:
$$ U_2 = -pE\cos 90^\circ = -pE 	imes 0 = 0 $$
Step 3:
Energy required to rotate by $90^\circ$:
$$ \Delta U = U_2 - U_1 = 0 - (-pE) = pE $$
Correct answer:
$ \boxed{pE} $
So, the right option is
Option A: $pE$
.

Answer

$pE$

Answer

$\mathrm{pE}^2$

Answer

$p^2 E$

Answer

infinity

Electrostats & Capacitance

An electric dipole of dipole moment ' p ' is aligned parallel to a uniform electric field ' E '. The energy required to rotate the dipole by 90^{\circ} is \left[\begin{array}{ll}\sin 0^{\circ}=0, & \sin 90^{\circ}=1 \\ \cos 0^{\circ}=1, & \cos 90^{\circ}=0\end{array}\right]

Choose the correct answer: