A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and magnetic fields is :
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In LC oscillation energy is transferred C to L
or L to C maximum energy in L is \( = \frac{1}{2}LI_{\max }^2\)
Maximum energy in C is \( = \frac{{q_{\max }^2}}{{2C}}\)
Equal energy will be when
\(\frac{1}{2}L{I^2} = \frac{1}{2}\frac{1}{2}LI_{\max }^2\)
\(I = \frac{1}{{\sqrt 2 }}{I_{\max }}\)
\(I = {I_{\max }}\sin \omega t = \frac{1}{{\sqrt 2 }}{I_{\max }}\)
\(\omega t = \frac{\pi }{4}\)
or \(\frac{{2\pi }}{T}t = \frac{\pi }{4}\) or \(t = \frac{\pi }{8}\)
\(t = \frac{\pi }{8}2\pi \sqrt {LC} = \frac{\pi }{4}\sqrt {LC} \)