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 (q) is

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

Hint:

Total energy is Q squared over 2C; set the electric energy equal to half of it.

Answer 1

The Correct Option is C

Step 1: Use the time dependence
The charge is $q = Q\cos\omega t$. The electric energy is $\dfrac{Q^2\cos^2\omega t}{2C}$ and the magnetic energy is $\dfrac{Q^2\sin^2\omega t}{2C}$.

Step 2: Equal energies
They are equal when $\cos^2\omega t = \sin^2\omega t$, so $\omega t = \frac{\pi}{4}$.

Step 3: Charge then
$q = Q\cos\frac{\pi}{4} = \dfrac{Q}{\sqrt{2}}$.

Step 4: Result
Option (C).

Final Answer:
The charge is Q/sqrt 2. This is option (C). \[ \boxed{\text{(C) }\frac{Q}{\sqrt{2}}} \]