An electric field of $1000 \mathrm{~V} / \mathrm{m}$ is applied to an electric dipole at angle of…
An electric field of $1000 \mathrm{~V} / \mathrm{m}$ is applied to an electric dipole at angle of $45^{\circ}$. The value of electric dipole moment is $10^{-29} \mathrm{C} \cdot \mathrm{m} .$ What is the potential energy of the electric dipole?
$-20 \times 10^{-18} \mathrm{~J}$
$-7 \times 10^{-27} \mathrm{~J}$
$-10 \times 10^{-29} \mathrm{~J}$
$-9 \times 10^{-20} \mathrm{~J}$
Solution
Potential energy of a dipole is given by $\mathrm{U}=-\overrightarrow{\mathrm{P}} \overrightarrow{\mathrm{E}}$
$=-P E \cos \theta$
[Where $\theta=$ angle between dipole and perpendicular to the field $=-\left(10^{-29}\right)\left(10^{3}\right) \cos 45^{\circ}$
$=-0.707 \times 10^{-26} \mathrm{~J}=-7 \times 10^{-27} \mathrm{~J}$