Q140 / 180 · KCET 2025 · Physics

Match Column-I with Column - II related to an electric dipole of dipole moment $\vec{p}$ that is placed in a uniform electric field $\overrightarrow{\mathrm{E}}$. \begin{array}{|l|l|l|l|}\hline \text{Column - I Angle between } \vec{p} \text{ and } \vec{E} & \text{Column - II Potential energy of the dipole} \\\hline a) 180^{\circ}& i) -pE \\ b) 120^{\circ}&ii) pE \\ c) 90^{\circ}&iii) \frac{1}{2} \mathrm{pE}\\ &iv) 0 \\\hline\end{array}

  • A
    $a-i, b-i i, c- iii$
  • B
    $a-i i, b-i i i, c-i$
  • C
    $a-i i, b-i, c-i v$
  • Correct answer
    D
    $a - ii, b - iii, c - iv$

Solution

PE of dipole $=\overrightarrow{-p} \cdot \vec{E}=-p E \cos \theta$ (a) $\theta=180^{\circ} \mathrm{PE}=-\mathrm{pE} \cos 180^{\circ}=\mathrm{pE} \rightarrow$ (ii) (b) $\theta=120^{\circ} \mathrm{PE}=-\mathrm{pE} \cos 120^{\circ}=-\mathrm{pE}\left(\frac{-1}{2}\right)=\frac{\mathrm{pE}}{2} \quad \rightarrow$ (iii) (c) $\theta=90^{\circ} \mathrm{PE}=-\mathrm{pE} \cos 90^{\circ}=0 \quad \rightarrow$ (iv) $\mathrm{a} \rightarrow$ (ii), $\mathrm{b} \rightarrow$ (iii), $\mathrm{c} \rightarrow$ (iv)

Hence, the correct answer is option: 'D'.

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