Given data

• Capacitance: $C = 500\,\mu F = 500 \times 10^{-6} F = 5 \times 10^{-4} F$
• Inductance: $L = 50\,mH = 50 \times 10^{-3} H = 5 \times 10^{-2} H$
• Initial charging voltage: $V = 100\,V$

Concept used

In an ideal LC circuit, the initial energy stored in the charged capacitor is completely transferred to the inductor when the current becomes maximum.

• Energy initially in capacitor: $U_C = \frac{1}{2}CV^2$
• Energy in inductor at maximum current: $U_L = \frac{1}{2}LI_{\max}^2$

At maximum current, $\frac{1}{2}CV^2 = \frac{1}{2}LI_{\max}^2$

Solve for maximum current

Cancelling $\frac{1}{2}$ from both sides: $CV^2 = LI_{\max}^2$

So, $I_{\max} = V\sqrt{\frac{C}{L}}$

Substitute values

$I_{\max} = 100\sqrt{\frac{5 \times 10^{-4}}{5 \times 10^{-2}}}$

$I_{\max} = 100\sqrt{10^{-2}}$

$I_{\max} = 100 \times 10^{-1} = 10\,A$

Final answer $\boxed{10}$

Comparison with stored answer

Stored correct answer = $10$

Our derived answer = $10$

Hence, they agree.