Question 804: Electrostats & Capacitance

Question

An electric dipole will have minimum potential energy when it subtends an angle
$$\left[\begin{array}{l}
\cos 0^{\circ}=1 \
\sin 0^{\circ}=0
\end{array}ight]\left[\begin{array}{l}
\cos 90^{\circ}=0 \
\cos \pi=-1
\end{array}ight]$$

Accepted Answer

The potential energy ($U$) of an electric dipole in an external uniform electric field ($\mathbf{E}$) is given by the expression:
$$ U = -\mathbf{p} \cdot \mathbf{E} = -pE \cos 	heta $$
where:
$\mathbf{p}$ is the electric dipole moment,
$E$ is the magnitude of the electric field,
$	heta$ is the angle between the dipole moment $\mathbf{p}$ and the electric field $\mathbf{E}$.
The potential energy is minimized when $\cos 	heta$ is maximized, which occurs when $\cos 	heta = 1$. This happens when $	heta = 0^\circ$, meaning the dipole moment is aligned with the electric field.
Therefore, the electric dipole will have minimum potential energy when it subtends an angle of zero with the direction of the field.
The correct option is: D) zero with the direction of the field.

Answer

$\pi$ with direction of field.

Answer

$\frac{\pi}{2}$ with direction of field.

Answer

$\frac{3 \pi}{2}$ with direction of field.

Answer

zero with direction of field.

Electrostats & Capacitance

An electric dipole will have minimum potential energy when it subtends an angle $\left[\begin{array}{l} \cos 0^{\circ}=1 \\ \sin 0^{\circ}=0 \end{array}\right]\left[\begin{array}{l} \cos 90^{\circ}=0 \\ \cos \pi=-1 \end{array}\right]

Choose the correct answer: