In an oscillating LC circuit the maximum charge on the capacitor is Q. The charges on the capacitor when the energy is stored equally between the electric and magnetic field is

Options

A. `Q/(sqrt(2))`
B. Q
C. `Q/(sqrt(3))`
D. `Q/2`

Answer

A

Explanation

Let Q be the maximum charge on the capacitor and the maximum energy `E = 1/2 (Q^2)/C`. When it is equally shared between the eleclric and magnetic fields, the energy stored in the capacitor = `1/2 [1/2 (Q^2)/(C)]` In this case , If q is the charge on the capacitor, then `1/2 (q^2)/(C) = 1/2 [1/2 (Q^2)/C]`.
`q^(2) = (Q^2)/C :. q=Q/(sqrt2)`.