Question

An electric field of 1000V/m is applied to an electric dipole at an electric dipole at an angle of $45{}^\circ $. The value of the electric dipole moment is \[{{10}^{-29}}C.m\]. What is the potential energy (in joule) of the electric dipole?

Answer 1

Hint:
Here we are directly given the value of electric field and dipole moment. We can use the formula for the potential energy i.e. \[ U(\theta )=-p.E\] to solve this question.



Formula used:
\[ U(\theta )=-p.E\]
\[U(\theta )=-pEcos\theta \]
Here p is the dipole moment and E electric field and $\theta$ is the angle between both of them


Complete answer:
Here electric field, dipole moment and angle between them is given,
\[\therefore U(\theta )=-p.E\]
\[\Rightarrow U(\theta )=-pEcos\theta \]
Now, according to the given question p=\[{{10}^{-29}}C.m\],$\theta =45{}^\circ $, $E=1000V/m$
Using the formula \[U(\theta )=-pEcos\theta \]
$U=(-{{10}^{29}})(1000)(\cos 45{}^\circ )$
$U=(-{{10}^{26}})(\dfrac{1}{\sqrt{2}})$
$U=-7\times {{10}^{26}}J$
Hence, the correct answer is $U=-7\times {{10}^{26}}J$


Note:When a dipole is placed in an electric field, the dipole experiences force due to the electric field, which causes it to rotate either clockwise or counterclockwise. This movement or work done stored in the form of potential energy which we have calculated in this question