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

Answer

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

### Step-by-Step Solution:

1. **Understanding the Energy in LC Circuit**:
- The total energy \( E \) in an LC circuit is conserved and can be expressed as the sum of the energy stored in the capacitor and the energy stored in the inductor:
\[ E = U_C + U_L \]
- The energy stored in the capacitor \( U_C \) is given by:
\[ U_C = \frac{1}{2} C V^2 = \frac{1}{2} \frac{Q^2}{C} \]
- The energy stored in the inductor \( U_L \) is given by:
\[ U_L = \frac{1}{2} L I^2 \]

2. **Condition for Equal Energy Distribution**:
- When the energy is equally distributed, we have:
\[ U_C = U_L \]
- Therefore, we can write:
\[ \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} L I^2 \]

3. **Relating Charge and Current**:
- The current \( I \) in the circuit can be expressed in terms of charge \( q \) on the capacitor:
\[ I = -\frac{dq}{dt} \]
- At the point where the energy is equally distributed, we can denote the charge on the capacitor as \( q \).

4. **Substituting the Charge**:
- At the point of equal energy distribution, we can express the energy in terms of charge \( q \):
\[ U_C = \frac{1}{2} \frac{q^2}{C} \]
\[ U_L = \frac{1}{2} L \left(-\frac{dq}{dt}\right)^2 \]
- Since \( U_C = U_L \), we can equate:
\[ \frac{1}{2} \frac{q^2}{C} = \frac{1}{2} L \left(-\frac{dq}{dt}\right)^2 \]

5. **Finding the Charge \( q \)**:
- Given that the maximum charge on the capacitor is \( Q \), we can find the charge when the energy is equally distributed:
\[ q = \frac{Q}{\sqrt{2}} \]

### Final Answer:
The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is:
\[ q = \frac{Q}{\sqrt{2}} \]