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

Answer 1

The correct option is C $\frac{Q}{\sqrt{2}}$

For LC circuit, $U_E+U_B=\frac{Q^2}{2C}$

Here $U_E=U_B$ and $U_E=\frac{q^2}{2C}$ where $q$ is the required charge on the capacitor.

So, $2U_E=\frac{Q^2}{2C}$

or $2\times \frac{q^2}{2C}=\frac{Q^2}{2C}$

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