KCET · Physics · Electrostatics
Match Column-I with Column - II related to an electric dipole of dipole moment \(\vec{p}\) that is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}\).
| Column - I Angle between \(\vec{p}\) and \(\vec{E}\) | Column - II Potential energy of the dipole |
| a. \(180^{\circ}\) | i. \(-pE\) |
| b. \(120^{\circ}\) | ii. \(pE\) |
| c. \(90^{\circ}\) | iii. \(\frac{1}{2} \mathrm{pE}\) |
| iv. \(0\) |
- A \(a-i, b-i i, c- iii\)
- B \(a-i i, b-i i i, c-i\)
- C \(a-i i, b-i, c-i v\)
- D \(a - ii, b - iii, c - iv\)
Answer & Solution
Correct Answer
(D) \(a - ii, b - iii, c - iv\)
Step-by-step Solution
Detailed explanation
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)
(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)
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