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\[\vec{E},\]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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