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: Understand the concept
In an LC circuit the total energy is constant and shifts between the capacitor (electric field) and the inductor (magnetic field). The total is \(\dfrac{Q^2}{2C}\), the energy when the capacitor holds its maximum charge \(Q\).

Step 2: Equal sharing
If the energy is shared equally, the electric part is half the total:
\[ \frac{q^2}{2C} = \frac{1}{2}\cdot\frac{Q^2}{2C} \]

Step 3: Solve
\[ q^2 = \frac{Q^2}{2} \Rightarrow q = \frac{Q}{\sqrt{2}} \]

Step 4: Check the options
\(q = Q\) means all the energy is electric, \(q = \frac{Q}{2}\) gives only a quarter of the energy in the capacitor, and \(q = \frac{Q}{\sqrt{3}}\) gives one third. The result is option (C).

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