Electrostatics 4 Question 3
3. 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 $10^{-29}$ $\mathrm{C}-\mathrm{m}$. What is the potential energy of the electric dipole?
(a) $-9 \times 10^{-20} \mathrm{~J}$
(b) $-10 \times 10^{-29} \mathrm{~J}$
(c) $-20 \times 10^{-18} \mathrm{~J}$
(d) $-7 \times 10^{-27} \mathrm{~J}$
(Main 2019, 11 Jan II)
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Answer:
Correct Answer: 3. (d)
Solution:
- Given,
$ \begin{aligned} & \mathbf{E}=1000 \mathrm{~V} / \mathrm{m} \\ & \theta=45^{\circ} and\\ & \mathbf{p}=10^{-29} \mathrm{C}-\mathrm{m} \end{aligned} $
We know that, electric potential energy stored in an electric dipole kept in uniform electric field is given by the relation
$ \begin{aligned} U & =-\mathbf{p} \cdot \mathbf{E}=-P E \cos \theta \\ & =-10^{-29} \times 1000 \times \cos 45^{\circ} \\ \Rightarrow \quad U & \approx-7 \times 10^{-27} \mathrm{~J} \end{aligned} $
