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 becomes

• A. \(\frac{Q}{\sqrt{2}}\)
• B. \(Q\sqrt{3}\)
• C. \(\frac{Q}{2}\)
• D. \(\frac{Q}{4}\)

Hint:

Total energy is conserved; equal sharing means each field holds half.

Answer 1

The Correct Option is A

Step 1: Use time dependence:
$q = Q\cos\omega t$. Electric energy is $\frac{Q^2}{2C}\cos^2\omega t$.

Step 2: Half the total:
Equal sharing needs $\cos^2\omega t = \frac12$, so $\cos\omega t = \frac{1}{\sqrt2}$ and $q = \frac{Q}{\sqrt2}$.

Final Answer:
$q = \frac{Q}{\sqrt{2}}$, option (A). \[ \boxed{\frac{Q}{\sqrt{2}}} \]