A) \[\sqrt{2}pE\]
B) \[\frac{pE}{2}\]
C) \[2pE\]
D) \[pE\]
Correct Answer: D
Solution :
When an electric dipole is placed in an electric field \[\overrightarrow{E}\], a torque \[\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}\] acts on it. This torque tries to rotate the dipole through an angle \[\theta \]. 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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