A) \[\sqrt{2}\,pE\]
B) \[\frac{pE}{2}\]
C) \[2\text{ }pE\]
D) pE
Correct Answer: D
Solution :
| [d] When an electric dipole is placed in an electric field \[\vec{E},\] a torque \[\vec{\tau }=\vec{p}\times \vec{E}\] acts on it. This torque tries to rotate the dipole through an angle. |
| If the dipole is rotated from an angle \[{{\theta }_{1}}\] to \[{{\theta }_{2}}\] then work done by external force is given by |
| \[W=pE(\cos {{\theta }_{1}}-\cos {{\theta }_{2}})\] ...(i) |
| putting \[{{\theta }_{1}}={{0}^{o}},\,\,{{\theta }_{2}}={{90}^{o}}\] in the Eq. (i), we get |
| \[W=pE(\cos {{0}^{o}}-\cos {{90}^{o}})\] |
| \[=pE\,\,(1-0)\] |
| \[=pE\] |
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