Question

In an oscillating LC circuit, the maximum charge on the capacitor is $Q$. The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is:

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

Answer 1

The correct option is B

$\frac{Q}{\sqrt{2}}$

Step 1: Given data

the maximum charge on the capacitor is $Q$ in an LC circuit.

Step 2: Formula used

Energy stored in a capacitor,

$E=\frac{1}{2}\frac{Q^2}{C}$

Step 3: To find

The charge on the capacitor, when the energy is stored equally between the electric and magnetic field

Step 4: Calculation

The total energy stored in a capacitor,

$E=\frac{1}{2}\frac{Q^2}{C}-------------\left(1\right)$

It is given that the energy is equally stored between the electric and magnetic field.

In this case,

$$\begin{gathered} \frac{E}{2}=\frac{1}{2}\frac{q^2}{C} \\ E=\frac{q^2}{C}--------------\left(2\right) \end{gathered}$$

From $\left(1\right)$ and $\left(2\right)$, we get

$$\begin{gathered} \frac{1}{2}\frac{Q^2}{C}=\frac{q^2}{C} \\ \Rightarrow q=\frac{Q}{\sqrt{2}} \end{gathered}$$

The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is $\frac{Q}{\sqrt{2}}$.

Hence, option B is correct.