Question

In an oscillating LC circuit the maximum charge on the capacitor is Q. When the charge is stored equally between the electric and magnetic fields, what is the charge on the capacitor?

Answer 1

Maximum charge of the capacitor= Q
So total energy of the circuit `=1/2Q^2/C`
When the charge of the capacitor is q, then energy stored in the electric fields is `1/2q^2/C`.At this stage energy stored in the magnetic field is `1/2Li^2`.
If it is equal to `1/2q^2/C`, then total energy
`=1/2q^2/C+1/2Li^2=1/2q^2/C+1/2q^2/C=q^2/C`
So, `q^2/C=1/2Q^2/C`or,`q^2=Q^2/2` or, `q=Q/sqrt2`