Electrostatics Question 301
Question: Two opposite and equal charges $ 4\times {{10}^{-8}}coulomb $ when placed $ 2\times {{10}^{-2}}cm $ away, form a dipole. If this dipole is placed in an external electric field $ 4\times 10^{8}newton/coulomb $ , the value of maximum torque and the work done in rotating it through $ 180{}^\circ $ will be [MP PET 1996]
Options:
A) $ 64\times {{10}^{-4}}Nm $ and $ 64\times {{10}^{-4}}J $
B) $ 32\times {{10}^{-4}} $ Nm and $ 32\times {{10}^{-4}}J $
C) $ 64\times {{10}^{-4}}Nm $ and $ 32\times {{10}^{-4}}J $
D) $ 32\times {{10}^{-4}}Nm $ and $ 64\times {{10}^{-4}}J $
Show Answer
Answer:
Correct Answer: D
Solution:
Dipole moment $ p=\text{4}\times \text{1}{{0}^{\text{8}}}~\times \text{2}\times \text{1}{{0}^{\text{4}}}=\text{ 8}\times \text{1}{{0}^{\text{12}}}m $
Maximum torque $ =pE=\text{8}\times \text{1}{{0}^{\text{12}}}\times \text{4}\times \text{1}{{0}^{\text{8}}} $
$ =\text{ 32}\times \text{1}{{0}^{\text{4}}}Nm $
Work done in rotating through $ \text{18}{{0}^{\text{o}}}=\text{ 2}pE $
$ =\text{ 2}\times \text{32}\times \text{1}{{0}^{\text{4}}}=\text{ 64}\times \text{1}{{0}^{\text{4}}}J $
