Question

In an oscillating $L-C$ 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 $\frac{Q}{\sqrt{2}}$

Total energy stored$=\frac{1}{2}\frac{Q^2}{C}$

At any time electrostatic energy is equal to magnetic energy.

$\frac{1}{2}\frac{Q^2}{C}=\frac{1}{2}\frac{q^2}{C}+\frac{1}{2}L{I}^2...............\left(1\right)$

Since $\frac{q^2}{2C}=\frac{{LI}^2}{2}$

Equation $\left(1\right)$ becomes,

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

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

Where $q$ is the charge on capacitor at this instant.