A) \[\text{2}.\text{65J}{{\text{m}}^{\text{-3}}}\]
B) \[\text{1}.\text{95J}{{\text{m}}^{\text{-3}}}\]
C) \[\text{1}.38\text{J}{{\text{m}}^{\text{-3}}}\]
D) \[0.69\,\text{J}{{\text{m}}^{\text{-3}}}\]
Correct Answer: C
Solution :
Energy density \[=\frac{Energy}{Volume}=\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}\] \[=\frac{1}{2}{{\varepsilon }_{0}}{{\left[ \frac{V}{d} \right]}^{2}}\] Here, as the dielectric is inserted between the plates and plates are connected to a voltage source. Energy density \[=\frac{1}{2}{{\varepsilon }_{0}}K{{\left[ \frac{V}{d} \right]}^{2}}\] Given, \[K=5,\,\,V=500\]volt, \[d=2\times {{10}^{-3}}m\] \[u=\frac{1}{2}\times 8.85\times {{10}^{-12}}\times 5\times {{\left[ \frac{500}{2\times {{10}^{-3}}} \right]}^{2}}\] \[=1.38\,J{{m}^{-3}}\]
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