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A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with adielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is\[3\times {{10}^{4}}V/m,\]the charge density of the positive plate will be close to :   JEE Main  Solved  Paper-2014

A) \[3\times {{10}^{4}}C/{{m}^{2}}\]            

B) \[6\times {{10}^{4}}C/{{m}^{2}}\]

C) \[6\times {{10}^{-7}}C/{{m}^{2}}\]          

D) \[3\times {{10}^{-7}}C/{{m}^{2}}\]

Correct Answer: C

Solution :

\[K=2.2\] \[d=5mm\]                         \[E=3\times {{10}^{4}}\frac{v}{m}\] \[\frac{\sigma }{k{{\in }_{0}}}=3\times {{10}^{4}}\] \[\sigma =k{{\in }_{0}}\times 3\times {{10}^{4}}\] \[=2.2\times 8.85\times {{10}^{-12}}\times 3\times {{10}^{4}}\] \[=58.41\times {{10}^{-8}}=5.84\times {{10}^{-7}}=6\times {{10}^{-7}}c/{{m}^{2}}\](approx.)