A) \[Q/2\]
B) \[Q/\sqrt{3}\]
C) \[Q/\sqrt{2}\]
D) \[Q\]
Correct Answer: C
Solution :
In an \[LC\] circuit the energy oscillates between inductor (in the magnetic field) and capacitor (in the electric field). \[{{U}_{E\,\,\max }}\][Maximum energy stored in capacitor] \[=\frac{{{Q}^{2}}}{2C}\] \[{{U}_{B\,\,\max }}\][Maximum energy stored in inductor] \[=\frac{Li_{0}^{2}}{2}\] where \[{{I}_{0}}\] is the current at this time. For the given instant\[{{U}_{E}}={{U}_{B}}\] \[ie,\] \[\frac{{{q}^{2}}}{2C}=\frac{L{{i}^{2}}}{2}\] From energy conservation \[{{U}_{E}}+{{U}_{B}}={{U}_{E\,\,\max }}={{U}_{B\,\,\max }}\] \[\Rightarrow \] \[2\frac{{{q}^{2}}}{2C}=\frac{{{Q}^{2}}}{2C}\] \[\Rightarrow \] \[q=\frac{Q}{\sqrt{2}}\]
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