A) \[64\times {{10}^{-4}}Nm\text{ }and\text{ }64\times {{10}^{-4}}J\]
B) \[32\times {{10}^{-4}}Nm\text{ }and\text{ }32\times {{10}^{-4}}J\]
C) \[64\times {{10}^{-4}}Nm\text{ }and\text{ }32\times {{10}^{-4}}J\]
D) \[32\times {{10}^{-4}}Nm\text{ }and\text{ }64\times {{10}^{-4}}J\]
Correct Answer: D
Solution :
Given, \[q=4\times {{10}^{-8}}C,\] \[2a=2\times {{10}^{-2}}cm\] \[=2\times {{10}^{-4}}m\] Electric dipole moment \[(p)=q\times 2a=4\times {{10}^{-8}}\times 2\times {{10}^{-4}}\] \[=8\times {{10}^{-12}}\text{C-m}\] \[E=4\times {{10}^{8}}N/C\] Torque acting on electric dipole in an electric field \[\tau =Ep\,\sin \,\theta \] Maximum torque \[{{\tau }_{\max }}=Ep\] \[=4\times {{10}^{8}}\times 8\times {{10}^{-12}}\] \[=32\times {{10}^{-4}}N\text{-m}\] Work done in rotating electric dipole through an angle \[\theta ,\] \[W=Ep(1-\cos \,\theta )\] \[{{W}_{{{180}^{o}}}}=Ep(1-\cos \,{{180}^{o}})=2Ep\] \[=64\times {{10}^{-4}}J\]
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