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

Explanation

To solve the problem, we need to determine the charge on the capacitor when the energy is equally distributed between the electric field and the magnetic field in an oscillating LC circuit.

### Step-by-Step Solution:

1. **Understand the Energy in the LC Circuit**:
The total energy \( U \) in an LC circuit is given by the formula:
\[ U = \frac{1}{2} Q^2 / C \]
where \( Q \) is the maximum charge on the capacitor and \( C \) is the capacitance.

2. **Condition for Equal Energy Distribution**:
When the energy is equally distributed between the electric field and the magnetic field, each field will have half of the total energy:
\[ U_{electric} = U_{magnetic} = \frac{U}{2} \]

3. **Energy in the Electric Field**:
The energy stored in the electric field when the charge on the capacitor is \( Q' \) is:
\[ U_{electric} = \frac{1}{2} \frac{(Q')^2}{C} \]

4. **Energy in the Magnetic Field**:
The energy stored in the magnetic field when the current is maximum (which occurs when the capacitor is half charged) is given by:
\[ U_{magnetic} = \frac{1}{2} L I^2 \]
At the point where the energy is equally distributed, we can relate the current \( I \) to the charge \( Q' \) on the capacitor. The current can be expressed in terms of charge as:
\[ I = -\frac{dQ}{dt} \]
At the point of equal energy distribution, the charge on the capacitor will be such that:
\[ U_{electric} = U_{magnetic} \]

5. **Setting Up the Equation**:
Since both energies are equal, we can set them equal to each other:
\[ \frac{1}{2} \frac{(Q')^2}{C} = \frac{1}{2} L I^2 \]
However, we know that when the energy is equally distributed, the charge \( Q' \) can be expressed as:
\[ Q' = \frac{Q}{\sqrt{2}} \]

6. **Final Charge Calculation**:
Therefore, the charge on the capacitor when the energy is equally distributed between the electric and magnetic fields is:
\[ Q' = \frac{Q}{\sqrt{2}} \]

### Conclusion:
The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is \( \frac{Q}{\sqrt{2}} \).