Question

In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor is q. The relation between Q and q is

• A. \(Q=q\)
• B. \(Q=\sqrt{2}q\)
• C. \(Q=\sqrt{3}q\)
• D. \(Q=2q\)

Hint:

Equal sharing means the capacitor holds half of the total energy, which equals the maximum capacitor energy.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In an LC circuit the total energy stays constant and equals the maximum electric energy \(\dfrac{Q^2}{2C}\).

Step 2: Equal sharing
The capacitor then holds half of it: \(\dfrac{q^2}{2C}=\dfrac{1}{2}\cdot\dfrac{Q^2}{2C}\).

Step 3: Solve
\(q^2=\dfrac{Q^2}{2}\Rightarrow Q=\sqrt{2}\,q\)

Final Answer:
The relation is \(Q=\sqrt{2}\,q\). \[ \boxed{\text{(B) }Q=\sqrt{2}q} \]