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: Understanding the Concept:
In an LC circuit, energy moves between the capacitor (electric energy \(\frac{q^2}{2C}\)) and the inductor (magnetic energy \(\frac12 Li^2\)). The total is constant and equals the maximum electric energy \(\frac{Q^2}{2C}\).

Step 2: Key Formula or Approach:
When the energy is shared equally, the electric energy is half the total.

Step 3: Detailed Explanation:
\(\frac{q^2}{2C} = \frac12\cdot\frac{Q^2}{2C}\).
So \(q^2 = \frac{Q^2}{2}\).
\[ q = \frac{Q}{\sqrt2} \]
Option C, \(\frac Q2\), would give only a quarter of the maximum electric energy.

Final Answer:
The charge is \(\frac{Q}{\sqrt{2}}\), option (A). \[ \boxed{\frac{Q}{\sqrt{2}}} \]