Question

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

Options

• Q/2

• `"Q"// sqrt2`

• `"Q"// sqrt3`

• Q/3

Answer 1

In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is `"Q"// sqrt2`.

Explanation:

Maximum energy stored in a capacitor,

`"E"_1 = ("Q"^2)/(2"C")`

When energy is stored equally between the electric and magnetic fields, then energy in the capacitor is `"E"_2 = 1/2  "E"_1`

If Q' is the charge on the capacitor in this case,

`"then"  "E"_2 = ("Q'"^2)/(2"C")`

`therefore "Q"^2/(2"C") = 1/2 "Q"^2/(2"C")`

`"Q'" = "Q"/sqrt2`